Question

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

Name: Problem 36, Chapter 1: Intermediate Algebra
Uploaded: 2020-06-15T09:57:29-08:00
Duration: 32 s
Channel: Ankit Gupta
Description: Solve the absolute value equations. -3|x-5|=7

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

Intermediate Algebra

Julie Miller, Molly… 5th Edition

Chapter 1, Problem 36

Instant Answer

Solved by Expert Ankit Gupta

06/15/2020

Step 1

We can do this by dividing both sides of the equation by -3. $$\frac{-3|x-5|}{-3} = \frac{7}{-3}$$ This simplifies to: $$|x-5| = -\frac{7}{3}$$ Show more…

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

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Key Concepts

Feasibility and Sign Constraints

Due to the nonnegative nature of absolute value expressions, multiplying them by a negative coefficient or equating them to a positive value can lead to infeasible equations. Recognizing these constraints can help in quickly determining when an absolute value equation has no solution.

Isolating Absolute Value Expressions

When solving equations with absolute value terms, it is important to isolate the absolute value on one side of the equation. This isolation allows us to apply the definition of absolute value, which typically requires considering separate cases based on whether the inner expression is positive or negative.

Absolute Value Properties

The absolute value of a number represents its distance from zero on the number line and is always nonnegative. This means that any expression inside the absolute value, regardless of its sign, will yield a result that is either zero or positive.

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