Question

Solve the absolute value equations. $$5|1-2 x|-7=3$$

Name: Problem 42, Chapter 1: Intermediate Algebra
Uploaded: 2020-06-15T10:00:07-08:00
Duration: 1 min 34 s
Channel: Ankit Gupta
Description: Solve the absolute value equations. 5|1-2 x|-7=3

   Solve the absolute value equations.
$$5|1-2 x|-7=3$$

Intermediate Algebra

Julie Miller, Molly… 5th Edition

Chapter 1, Problem 42

Instant Answer

Solved by Expert Ankit Gupta

06/15/2020

Step 1

We can do this by adding 7 to both sides of the equation: $$5|1-2x|-7+7=3+7$$ which simplifies to: $$5|1-2x|=10$$ Show more…

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Solve the absolute value equations. $$5|1-2 x|-7=3$$

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Key Concepts

Absolute Value Function

The absolute value function returns the non-negative distance of a number from zero, regardless of its sign. This is key in understanding that when an absolute value expression is involved in an equation, the output is always non-negative.

Case Analysis in Absolute Value Equations

When solving equations that include an absolute value, it is necessary to consider both the positive and negative possibilities of the expression inside the absolute value. This involves setting the inner expression equal to the positive value and the negative value of the target result after isolating the absolute expression.

Algebraic Manipulation

Before applying case analysis, algebraic techniques are used to isolate the absolute value expression in the equation. This involves performing operations such as addition, subtraction, multiplication, or division to simplify the equation into a form suitable for further analysis.

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