Question

Solve $\left|\frac{2 x-4}{12}\right|=5$.

Name: Problem 115, Chapter 6: Intermediate Algebra for College Students
Uploaded: 2020-09-04T05:51:12-08:00
Duration: 1 min 1 s
Channel: Suman Saurav Thakur
Description: Solve |(2 x-4)/(12)|=5.

   Solve $\left|\frac{2 x-4}{12}\right|=5$.

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 6, Problem 115

Instant Answer

Solved by Expert Suman Saurav Thakur

09/04/2020

Step 1

$\frac{2x-4}{12} = 5$ and $\frac{2x-4}{12} = -5$ Show more…

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Solve $\left|\frac{2 x-4}{12}\right|=5$.

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Key Concepts

Absolute Value

This concept is about the magnitude of a number regardless of its sign. In an equation, the absolute value represents the non-negative distance from zero, which requires considering both the positive and negative scenarios of the expression inside the absolute value.

Case Analysis

When solving an absolute value equation, the equation is typically split into two separate cases based on the definition of absolute value: one case where the expression inside the absolute value is non-negative, and another where it is negative. This ensures that all potential solutions are considered.

Linear Equations

After breaking down an absolute value equation into different cases, each case often leads to a linear equation. Solving these linear equations involves isolating the variable and applying standard algebraic operations, such as addition, subtraction, multiplication, and division.

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