Tiger Algebra/core — Spanish @ Weblate: <h3>Absolute value</h3> Absolute value (sometimes called modulus or magnitude) is …

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<h3>Absolute value</h3>

Absolute value (sometimes called modulus or magnitude) is how far a number, term, polynomial, or expression is from zero, regardless of whether it is positive or negative. For example: <math>4</math> and <math>-4</math> are the same distance from <math>0</math>, so they both have an absolute value of <math>4</math>.<br><br>

<img width="500" alt="Absolute value" src="https://user-images.githubusercontent.com/56831176/146247143-c8db661d-83ab-457f-9087-e9bc5cfa4ba3.png"><br>

Absolute value is represented by two bars, one of each side of the number, term, polynomial, or expression. For example, the absolute value of <math>-4</math> would be written as <math>|-4|</math><br><br>

<h3>Properties of absolute values</h3>
<ul>
<li>Non-negativity: <math>|x|≥0</math><br>
Absolute value is always non-negative, meaning it <b>always</b> yields zero or a positive.</li><br>
<li><math>|x|=\sqrt{x^2}</math>: Squaring a number makes it positive (or zero if the number is zero), and by taking the square root of a squared number we get a positive solution (or zero if the number is zero). This only works when <math>x</math> is a real number.</li><br>
<li>Multiplicativity: <math>|x\cdot y|=|x|\cdot|y|</math><br>
The absolute value of a product of two numbers equals the product of the absolute value of each number.</li><br>
<li>Subadditivity: <math>|x+y|≤|x|+|y|</math><br>
The absolute value of the sum of two real numbers is less than or equal to the sum of the absolute values of the two numbers.</li><br>
<li><math>|x|=y → x=\pm y</math> or <math>|x|=\pm x</math>: If the absolute value of <math>x</math> equals <math>y</math> then <math>x</math> equals plus or minus <math>y</math>. This rule is used for solving most absolute value questions.</li>
</ul>
<br><br>

<h3>Absolute value equations</h3>

Absolute value equations are equations in which the variable is within an absolute value operator.<br>
For example: <math>|x-4|=10</math><br>
Because the value of <math>x-4</math> can be <math>10</math> or <math>-10</math>, both of which have an absolute value of <math>10</math>, we need to consider both cases: <math>x-4=10</math> and <math>x-4=-10</math>. This can also be written as <math>x-4=\pm10</math>.<br><br>

So, <math>|x-4|=10</math> has two solutions:<br>
<math>x-4=10</math> → <math>x=14</math><br>
<math>x-4=-10</math> → <math>x=-6</math><br><br>

Because absolute values are always non-negative, it is possible to have equations with no solutions.<br>
For example: <math>|x - 5|=-9</math><br><br>

Absolute Value Equations and Inequalities are solved and explained step by step by the Tiger Algebra Absolute Value module.

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Key	English	Spanish
ScientificNotationSolverStep1TextUnit1SNI	{Step1OriginalEquationSNI}	{Step1OriginalEquationSNI}
ScientificNotationSolverStep1TextUnit2SNI	The exponent is -{Step1PowerOfTenNumberSNI}, making it 10 to the power of negative {Step1PowerOfTenNumberSNI}. When an exponent is negative, the solution is a number less than the origin or base number. To find our answer, we move the decimal to the left {Step1PowerOfTenNumberSNI} times:	El exponente es -{Step1PowerOfTenNumberSNI}, por lo que es 10 a la potencia de menos {Step1PowerOfTenNumberSNI}. Cuando un exponente es negativo, la solución es un número menor que el número de origen o de base. Para averiguar nuestra respuesta, movemos el decimal a la izquierda {Step1PowerOfTenNumberSNI} vez/veces:
ScientificNotationSolverStep1TextUnit3SNI	{Step1OriginalNumberSNI} -> {Step1OriginalNumberSolvedSNI}	{Step1OriginalNumberSNI} -> {Step1OriginalNumberSolvedSNI}
ScientificNotationSolverStep2Title1SNI	Final result	Resultado final
ScientificNotationSolverStep2TextUnit1SNI	{Step2FinalResultSNI}	{Step2FinalResultSNI}
ScientificNotationSolverStep1Title1ZI	0 can be written in more than one way in scientific notation	El 0 puede escribirse de varias formas en notación científica:
ScientificNotationSolverStep1TextUnit1ZI	{Step1FinalResultZI}	{Step1FinalResultZI}
ScientificNotationSolverStep1Title1NB1A10	Define the power of 10	Definir la potencia de 10
ScientificNotationSolverStep1TextUnit1NB1A10	The absolute value of {Step1OriginalNumberNB1A10} is between 1 and 10, so the original number stays the same because the power of 10 is 1 and 0 is the exponent.	El valor absoluto de {Step1OriginalNumberNB1A10} está entre 1 y 10, así que el número original no cambia porque la potencia de 10 es 1 y 0 es el exponente.
ScientificNotationSolverStep1TextUnit2NB1A10	{Step1OriginalNumberSolved1NB1A10}	{Step1OriginalNumberSolved1NB1A10}
ScientificNotationSolverStep2Title1NB1A10	Final result	Resultado final
ScientificNotationSolverStep2TextUnit1NB1A10	{Step2FinalResultNB1A10}	{Step2FinalResultNB1A10}
ScientificNotationSolverFinalResultSpokenDescription	The final result is {SolutionFinalResult}	El resultado final es {SolutionFinalResult}
AbsoluteValueEquations	Absolute value equations	Ecuaciones con valores absolutos
AbsoluteValueInequalities	Absolute value inequalities	Desigualdades con valores absolutos
AbsoluteValueEquationsContent	<h3>Absolute value</h3> Absolute value (sometimes called modulus or magnitude) is how far a number, term, polynomial, or expression is from zero, regardless of whether it is positive or negative. For example: <math>4</math> and <math>-4</math> are the same distance from <math>0</math>, so they both have an absolute value of <math>4</math>.<br><br> <img width="500" alt="Absolute value" src="https://user-images.githubusercontent.com/56831176/146247143-c8db661d-83ab-457f-9087-e9bc5cfa4ba3.png"><br> Absolute value is represented by two bars, one of each side of the number, term, polynomial, or expression. For example, the absolute value of <math>-4</math> would be written as <math>\|-4\|</math><br><br> <h3>Properties of absolute values</h3> <ul> <li>Non-negativity: <math>\|x\|≥0</math><br> Absolute value is always non-negative, meaning it <b>always</b> yields zero or a positive.</li><br> <li><math>\|x\|=\sqrt{x^2}</math>: Squaring a number makes it positive (or zero if the number is zero), and by taking the square root of a squared number we get a positive solution (or zero if the number is zero). This only works when <math>x</math> is a real number.</li><br> <li>Multiplicativity: <math>\|x\cdot y\|=\|x\|\cdot\|y\|</math><br> The absolute value of a product of two numbers equals the product of the absolute value of each number.</li><br> <li>Subadditivity: <math>\|x+y\|≤\|x\|+\|y\|</math><br> The absolute value of the sum of two real numbers is less than or equal to the sum of the absolute values of the two numbers.</li><br> <li><math>\|x\|=y → x=\pm y</math> or <math>\|x\|=\pm x</math>: If the absolute value of <math>x</math> equals <math>y</math> then <math>x</math> equals plus or minus <math>y</math>. This rule is used for solving most absolute value questions.</li> </ul> <br><br> <h3>Absolute value equations</h3> Absolute value equations are equations in which the variable is within an absolute value operator.<br> For example: <math>\|x-4\|=10</math><br> Because the value of <math>x-4</math> can be <math>10</math> or <math>-10</math>, both of which have an absolute value of <math>10</math>, we need to consider both cases: <math>x-4=10</math> and <math>x-4=-10</math>. This can also be written as <math>x-4=\pm10</math>.<br><br> So, <math>\|x-4\|=10</math> has two solutions:<br> <math>x-4=10</math> → <math>x=14</math><br> <math>x-4=-10</math> → <math>x=-6</math><br><br> Because absolute values are always non-negative, it is possible to have equations with no solutions.<br> For example: <math>\|x - 5\|=-9</math><br><br> Absolute Value Equations and Inequalities are solved and explained step by step by the Tiger Algebra Absolute Value module.	El valor absoluto de un número, representado entre dos barras, se puede considerar como el número de unidades entre dicho número y cero en la recta numérica, esté a la derecha o a la izquierda del cero, y es siempre un número entero positivo. <br><br> Las ecuaciones y desigualdades con valores absolutos se resuelven y explican paso a paso en el módulo de valor absoluto de Tiger Algebra.
AddingSubtractingFindingLeastCommonMultiple	Adding subtracting finding least common multiple	Sumar, restar y averiguar el mínimo común múltiplo
AddingSubtractingFindingLeastCommonMultipleContent	The Tiger Algebra Solver shows you how to add and subtract fractions and how to find their least common multiple for example:	Tiger Algebra te enseña a sumar y restar fracciones, así como a averiguar su mínimo común múltiplo, por ejemplo:
ApproximationTopic	Approximation	Aproximación
Approximation	Approximation	Aproximación
ApproximationContent	Approximation in mathematics is defined as a quantity close in value to but not the same as a desired quantity. Two mathematical symbols denote approximate equality: a wavy equal sign (≈) and a dotted equal sign (≒ or ≓). <br><br> Approximation is often used when an precise form or integer is not known or easily obtainable as well as with irrational numbers, such as π. Approximation can turn a complex calculation, for example, involving decimals into one that uses integers, or whole numbers, making it easier to solve. This is achieved by rounding the decimal values before performing any further operations.	La aproximación en matemáticas se define como una cantidad parecida en valor, pero no igual a la cantidad deseada. Hay dos símbolos matemáticos que denotan una igualdad aproximada: un signo igual ondulado (≈) y un signo igual punteado (≒ o ≓). <br><br> La aproximación se usa a menudo cuando una fórmula precisa o un número entero no se conocen o son difíciles de determinar, o también con los números irracionales como π. La aproximación puede convertir un cálculo complejo, por ejemplo, que contenga decimales, en uno que utilice números enteros, facilitando así su resolución. Esto se consigue redondeando los valores decimales antes de realizar las demás operaciones.
ArithmeticSequence	Arithmetic sequences	Progresión aritmética
ArithmeticSequenceContent	An arithmetic sequence, or arithmetic progression, is a set of numbers in which the difference between consecutive terms (terms that come after one another) is constant. This difference is called the common difference. For example, all of the consecutive terms in the arithmetic sequence:<br> <b><math>1, 4, 7, 10, 13, 16, 19, . . .</math></b><br> share a common difference of <math>3</math>.<br> Note: The three dots (. . .) mean that this sequence is infinite.<br><br> Though others can also be used, the following variables are typically used to represent the terms of an arithmetic sequence:<br> <math>a_1</math> represents the first term of the sequence. In the example above, <math>a_1=1</math><br> <math>a_n</math> represents the nth term (a term we are trying to find).<br> <math>d</math> represents the common difference between consecutive terms. In the example above, <math>d=3</math><br> <math>n</math> represents the number of terms in the sequence. In the example above, <math>n=7</math><br><br> The standard form of arithmetic sequences can be expressed as: <math>a, a+d, a+2d, a+3d, a+4d, a+5d . . .</math><br> <math>a</math> represents the first term and is sometimes written as <math>a_1</math>.<br> <math>d</math> represents the common difference.<br><br> <b>Formulas</b><br><br> <b>Finding any term (<math>a_n</math>) in an arithmetic sequence:</b><br> <b><math>a_n=a+d(n-1)</math></b><br><br> <math>a\:</math> represents the first term.<br> <math>d\:</math> represents the common difference.<br> <math>n\:</math> represents the position of a term in the sequence.<br> A sequence with <math>\:n\:</math> number of terms would be written as:<br> <math>a, a+d(2-1), a+d(3-1), a+d(4-1), a+d(5-1), a+d(6-1) ... a+d(n-1)</math><br> in which the last term's common difference is multiplied by <math>\:n-1\:</math> (because <math>\:d\:</math> is not used in the 1st term).<br><br> Example: To find the next term in:<br> <math>1, 4, 7, 10, 13, 16, 19...</math><br> which would be the 8th term, we would plug the following into the general term formula <math>\:a_n= a+d(n-1)</math>:<br> <math>a\:</math> (first term) <math> =1</math><br> <math>d\:</math> (common difference) <math> =3</math><br> <math>n\:</math> (term number) <math> =8</math><br> This would give us:<br> <math>a_8=1+3(8-1)\:</math> which we could solve to get <math>\:a_8=22</math>.<br> So, our sequence would be: <math>\:1, 4, 7, 10, 13, 16, 19, 22...</math><br><br> <b>Finding the sum of all the terms in an arithmetic sequence:</b><br> <b><math>s=n(a_1+a_n)/2</math></b><br><br> <math>s\:</math> is the sum of the terms in the sequence.<br> <math>a\:</math> represents the first term.<br> <math>n\:</math> represents the position of a term in the sequence.<br> <math>d\:</math> represents the common difference.<br> Example: To find the sum of:<br> <math>1, 4, 7, 10, 13, 16, 19...\:</math> we plug the following into the sum formula <math>\:s=n(a_1+a_n)/2</math> :<br> <math>n\:</math> (total number of terms)<math> =7</math><br> <math>a\:</math> (first term)<math> =1</math><br> <math>a_n\:</math> (the last term)<math> =19</math><br> This would give us:<br> <math>s=7(1+19)/2\:</math> which we could solve to get <math>\:s=70</math>.<br> So, the sum of the sequence would be: <math>\:70</math><br> Tiger identifies arithmetic sequences and displays their terms, the sum of their terms, and their explicit and recursive forms.	Una secuencia, sucesión o progresión aritmética es un conjunto de números en los que la diferencia entre los términos consecutivos (términos que van uno tras otro) es constante. Por ejemplo, todos los términos consecutivos en la secuencia aritmética:<br><b> 1, 4, 7, 10, 13, 16, 19, . . .</b><br> tienen una diferencia común de 3.<br><br>Aunque es posible utilizar otras variables, por lo general, usamos las siguientes para representar los términos de una secuencia aritmética:<br> <b>a1</b> representa el primer término de la secuencia;<br> <b>an</b> representa el término enésimo (el término que estamos intentando averiguar);<br> <b>d</b> representa la distancia común entre los términos consecutivos;<br> <b>n</b> representa el número de términos en la secuencia.<br><br>Tiger identifica las secuencias aritméticas y muestra sus términos, la suma de sus términos y su formas explícita y recursiva.
BasicComplexOperations	Basic complex operations	Operaciones básicas con números complejos
BasicComplexOperationsContent	A complex number is a number that can be expressed in the form <math>a + bi</math>, where a and b are real numbers and i is the imaginary unit, that satisfies the equation <math>x^2=−1</math>, that is, <math>i^2=−1</math>. In this expression, a is the real part and b is the imaginary part of the complex number. <br><br> The Tiger Algebra Calculator performs the basic operations on complex/imaginary numbers and shows you the step by step solution.	Un número complejo es aquel que puede expresarse en la forma <math>a + bi</math>, donde a y b son números reales e i es la unidad imaginaria, que satisface la ecuación <math>x^2=−1</math>, es decir, <math>i^2=−1</math>. En esta expresión, a es la parte real y b es la parte imaginaria del número complejo. <br><br> La calculadora de álgebra Tiger realiza las operaciones básicas de números complejos/imaginarios y muestra la solución paso a paso.
CancelingOut	Canceling out	Reducir fracciones
CancelingOutContent	When simplifying fractions you can sometimes divide the top (NUMERATOR) and bottom (DENOMINATOR) of a fraction by the same number. This simplification of a fraction is referred to as canceling out/down . Common problems require you to write a fraction in its simplest terms. To achieve that, you must keep canceling the fraction until it cannot be cancelled anymore. <br><br> The Tiger Algebra Solver and Calculator can help you check your answers when canceling out.	Para simplificar fracciones, a veces se puede dividir la parte de arriba (NUMERADOR) y la parte de abajo (DENOMINADOR) por el mismo número. Esta simplificación se llama reducir una fracción. Los problemas más usuales requieren que escribas una fracción en sus términos más simples. Para conseguirlo, debes reducir progresivamente la fracción hasta que ya no pueda reducirse más. <br><br> Tiger Algebra puede ayudarte a comprobar tus respuestas cuando reduzcas una fracción.
CircleTopic	Circle from equation	Circunferencia a partir de ecuación
CircleContent	In geometry, a circle is a shape made up of all the points on a plane at a fixed distance around a given point (the center). The equation for a circle is <math>(x-h)^2+(y-k)^2=r^2</math>, in which <math>h</math> and <math>k</math> represent the circle's center and <math>r</math> represents the circle's radius, the distance from the circle's center to any point on its perimeter. A circle with a center at <math>(4,5)</math> and a radius of <math>10</math>, for example, could be expressed as <math>(x-4)^2+(y-5)^2=100</math> <br> <img src="/images/circleImg1.png" alt="circle graph"> <br> <img src="/images/circleImg2.png" alt="circle related terms diameter, radius, chord, secant, tangent"> <br> <b>Relevant terms:</b><br> <ul> <li><b>Center</b>: The point around which a circle is formed. All points on a circle's perimeter are the same distance from the circle's center.</li><br> <li><b>Circumference</b>: The distance around a circle.</li><br> <li><b>Radius</b>: A line segment that lies between the center of a circle and any point on the circle's perimeter</li>.<br> <li><b>Diameter</b>: A line segment that lies between two points on a circle's perimeter and runs through the circle's center. It is equal to two times the circle's radius.</li><br> <li><b>Chord</b>: A line segment that lies between two points on a circle's perimeter and does not run through the circle's center.</li><br> <li><b>Secant</b>: A line that intersects two points on a circle's perimeter.</li><br> <li><b>Tangent</b>: A line that intersects one point on a circle's perimeter.</li> </ul>	En geometría, una circunferencia es una forma constituida por todos los puntos de un plano que se encuentran a una distancia fija de un punto definido (el centro). La ecuación para una circunferencia es <mah>((x-h)^2)+((y-k)^2)=r^2</math>, donde (h,k) representa el centro de la circunferencia y r el radio de la circunferencia, es decir, la distancia desde el centro de la circunferencia a cualquier punto de su perímetro. Por ejemplo, una circunferencia con su centro en (4,5) y un radio de 10, podría expresarse como </mah>((x-4)^2)+((y-5)^2)=100</math>. <br> <img src="/images/circleImg1.png" alt="circle graph"> <br> <img src="/images/circleImg2.png" alt="circle related terms diameter, radius, chord, secant, tangent"> <br> Términos importantes: <ul> <li>Centro: el punto alrededor del cual se forma una circunferencia. Todos los puntos del perímetro de una circunferencia están a la misma distancia del centro de la misma.</li> <li>Perímetro: la distancia alrededor de una circunferencia.</li> <li>Radio: segmento de recta entre el centro de una circunferencia y cualquiera de los puntos de su perímetro.</li> <li>Diámetro: segmento de recta entre dos puntos del perímetro de una circunferencia pasando por el centro de la circunferencia. Equivale a dos veces el radio.</li> <li>Cuerda: segmento de recta entre dos puntos del perímetro de una circunferencia sin pasar por el centro de esta.</li> <li>Secante: recta que corta dos puntos del perímetro de una circunferencia.</li> <li>Tangente: recta que corta un punto del perímetro de una circunferencia.</li> </ul>
Combination	Combination	Combinaciones
CombinationTopic	Combination	Combinaciones

Key	English	Spanish
About	About	Acerca de
AbsoluteValue	Absolute Value	Valor absoluto
AbsoluteValueEquations	Absolute value equations	Ecuaciones con valores absolutos
AbsoluteValueEquationsContent	<h3>Absolute value</h3> Absolute value (sometimes called modulus or magnitude) is how far a number, term, polynomial, or expression is from zero, regardless of whether it is positive or negative. For example: <math>4</math> and <math>-4</math> are the same distance from <math>0</math>, so they both have an absolute value of <math>4</math>.<br><br> <img width="500" alt="Absolute value" src="https://user-images.githubusercontent.com/56831176/146247143-c8db661d-83ab-457f-9087-e9bc5cfa4ba3.png"><br> Absolute value is represented by two bars, one of each side of the number, term, polynomial, or expression. For example, the absolute value of <math>-4</math> would be written as <math>\|-4\|</math><br><br> <h3>Properties of absolute values</h3> <ul> <li>Non-negativity: <math>\|x\|≥0</math><br> Absolute value is always non-negative, meaning it <b>always</b> yields zero or a positive.</li><br> <li><math>\|x\|=\sqrt{x^2}</math>: Squaring a number makes it positive (or zero if the number is zero), and by taking the square root of a squared number we get a positive solution (or zero if the number is zero). This only works when <math>x</math> is a real number.</li><br> <li>Multiplicativity: <math>\|x\cdot y\|=\|x\|\cdot\|y\|</math><br> The absolute value of a product of two numbers equals the product of the absolute value of each number.</li><br> <li>Subadditivity: <math>\|x+y\|≤\|x\|+\|y\|</math><br> The absolute value of the sum of two real numbers is less than or equal to the sum of the absolute values of the two numbers.</li><br> <li><math>\|x\|=y → x=\pm y</math> or <math>\|x\|=\pm x</math>: If the absolute value of <math>x</math> equals <math>y</math> then <math>x</math> equals plus or minus <math>y</math>. This rule is used for solving most absolute value questions.</li> </ul> <br><br> <h3>Absolute value equations</h3> Absolute value equations are equations in which the variable is within an absolute value operator.<br> For example: <math>\|x-4\|=10</math><br> Because the value of <math>x-4</math> can be <math>10</math> or <math>-10</math>, both of which have an absolute value of <math>10</math>, we need to consider both cases: <math>x-4=10</math> and <math>x-4=-10</math>. This can also be written as <math>x-4=\pm10</math>.<br><br> So, <math>\|x-4\|=10</math> has two solutions:<br> <math>x-4=10</math> → <math>x=14</math><br> <math>x-4=-10</math> → <math>x=-6</math><br><br> Because absolute values are always non-negative, it is possible to have equations with no solutions.<br> For example: <math>\|x - 5\|=-9</math><br><br> Absolute Value Equations and Inequalities are solved and explained step by step by the Tiger Algebra Absolute Value module.	El valor absoluto de un número, representado entre dos barras, se puede considerar como el número de unidades entre dicho número y cero en la recta numérica, esté a la derecha o a la izquierda del cero, y es siempre un número entero positivo. <br><br> Las ecuaciones y desigualdades con valores absolutos se resuelven y explican paso a paso en el módulo de valor absoluto de Tiger Algebra.
AbsoluteValueInequalities	Absolute value inequalities	Desigualdades con valores absolutos
AbsoluteValueInequalitiesContent	<div style="white-space: normal;"> <p>Absolute value inequalities are mathematical expressions that involve the absolute value function and inequalities. The absolute value of a real number represents its distance from zero on the number line. Inequalities involving absolute values often require different approaches than regular inequalities due to the non-linear nature of the absolute value function.</p> <h2>Basic Concepts</h2> <p>To understand absolute value inequalities, it's crucial to grasp the concept of absolute value. For any real number x, the absolute value of x, denoted as \|x\|, is defined as:</p> <p>\|x\| = x if x ≥ 0, and \|x\| = -x if x < 0.</p> <p>When solving absolute value inequalities, we often encounter expressions in the form \|ax + b\| < c or \|ax + b\| > c, where a, b, and c are real numbers.</p> <h2>Solving Absolute Value Inequalities</h2> <p>To solve absolute value inequalities, we typically follow these steps:</p> <ol> <li>Isolate the absolute value expression if it's not already isolated.</li> <li>Set up two inequalities without absolute values by considering both positive and negative cases.</li> <li>Solve each inequality separately.</li> <li>Combine the solutions if needed and represent the final solution on the number line.</li> </ol> <h2>Examples</h2> <p>Let's consider a few examples to illustrate the process of solving absolute value inequalities:</p> <h3>Example 1:</h3> <p>Solve the inequality \|2x - 3\| < 5.</p> <p>We start by isolating the absolute value expression:</p> <p>\|2x - 3\| < 5</p> <p>Then, we set up two inequalities:</p> <p>-5 < 2x - 3 < 5</p> <p>and</p> <p>-5 < -2x + 3 < 5</p> <p>We solve each inequality separately and combine the solutions to obtain the final solution.</p> <h3>Example 2:</h3> <p>Solve the inequality \|3x + 2\| >= 7.</p> <p>We follow similar steps as in Example 1 to solve this absolute value inequality.</p> <h2>Conclusion</h2> <p>Absolute value inequalities are important in various fields of mathematics and real-life applications. Mastering the techniques to solve them is essential for a deeper understanding of algebra and related subjects.</p> </div>	<div style="white-space: normal;"> <p>Las desigualdades de valor absoluto son expresiones matemáticas que involucran la función de valor absoluto y las desigualdades. El valor absoluto de un número real representa su distancia desde cero en la línea de los números. Las desigualdades que involucran valores absolutos a menudo requieren enfoques diferentes a las desigualdades regulares debido a la naturaleza no lineal de la función de valor absoluto.</p> <h2>Conceptos Básicos</h2> <p>Para entender las desigualdades de valor absoluto, es crucial comprender el concepto de valor absoluto. Para cualquier número real x, el valor absoluto de x, denotado como \|x\|, se define como:</p> <p>\|x\| = x si x ≥ 0, y \|x\| = -x si x < 0.</p> <p>Cuando resolvemos desigualdades de valor absoluto, a menudo encontramos expresiones en la forma \|ax + b\| < c o \|ax + b\| > c, donde a, b, y c son números reales.</p> <h2>Resolviendo Desigualdades de Valor Absoluto</h2> <p>Para resolver desigualdades de valor absoluto, generalmente seguimos estos pasos:</p> <ol> <li>Aislar la expresión de valor absoluto si aún no está aislada.</li> <li>Establecer dos desigualdades sin valores absolutos considerando ambos casos, positivo y negativo.</li> <li>Resolver cada desigualdad por separado.</li> <li>Combinar las soluciones si es necesario y representar la solución final en la línea numérica.</li> </ol> <h2>Ejemplos</h2> <p>Consideremos algunos ejemplos para ilustrar el proceso de resolución de desigualdades de valor absoluto:</p> <h3>Ejemplo 1:</h3> <p>Resuelve la desigualdad \|2x - 3\| < 5.</p> <p>Comenzamos aislando la expresión de valor absoluto:</p> <p>\|2x - 3\| < 5</p> <p>Luego, establecemos dos desigualdades:</p> <p>-5 < 2x - 3 < 5</p> <p>y</p> <p>-5 < -2x + 3 < 5</p> <p>Resolvemos cada desigualdad por separado y combinamos las soluciones para obtener la solución final.</p> <h3>Ejemplo 2:</h3> <p>Resuelve la desigualdad \|3x + 2\| >= 7.</p> <p>Seguimos pasos similares como en el Ejemplo 1 para resolver esta desigualdad de valor absoluto.</p> <h2>Conclusión</h2> <p>Las desigualdades de valor absoluto son importantes en varios campos de las matemáticas y aplicaciones de la vida real. Dominar las técnicas para resolverlas es esencial para una comprensión más profunda del álgebra y materias relacionadas.</p> </div>
AbsoluteValueProblem	Absolute value expressions	Expresiones con valores absolutos
AbsoluteValueProblem.plugin	simplifying absolute value expressions	Simplificar expresiones con valores absolutos
AdBlockConfirm	Okay, I'll Whitelist	Vale, lo incluiré en la lista blanca
AdBlockDetected	AdBlock Detected!	AdBlock detectada!
AdBlockMessage	Our website is made possible by displaying ads to our visitors. Please supporting us by whitelisting our website.	Nuestro sitio web es posible al mostrar anuncios a nuestros visitantes. Por favor, ayúdenos agregando nuestro sitio web a la lista blanca.
AddingSubtractingFindingLeastCommonMultiple	Adding subtracting finding least common multiple	Sumar, restar y averiguar el mínimo común múltiplo
AddingSubtractingFindingLeastCommonMultipleContent	The Tiger Algebra Solver shows you how to add and subtract fractions and how to find their least common multiple for example:	Tiger Algebra te enseña a sumar y restar fracciones, así como a averiguar su mínimo común múltiplo, por ejemplo:
AddSubLogs	Adding and subtracting logarithms	Sumar y restar logaritmos
AddSubLogs.plugin	adding and subtracting logarithms	sumar y restar logaritmos
AddSubLogsResultTypeDecimal	Decimal form:	Forma decimal:
AddSubLogsResultTypeZeroBaseUndefined	log 0 is undefined	el logaritmo de 0 es indefinido
AddSubLogsStep1Title	Add/Subtract the logarithms	Sumar y restar los logaritmos

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core/TigerAlgebra.Localization/Resources/TigerSharedResource.es.resx, string 429