Question

Solve. $$ |3 a-1|=|2 a+4| $$

Name: Problem 57, Chapter 8: Elementary and Intermediate Algebra
Uploaded: 2020-05-15T16:54:26-08:00
Duration: 54 s
Channel: Cory Kuzinski
Description: Solve. |3 a-1|=|2 a+4|

   Solve.
$$
|3 a-1|=|2 a+4|
$$

Elementary and Intermediate Algebra

Marvin L. Bittinger,… 4th Edition

Chapter 8, Problem 57

Instant Answer

Solved by Expert Cory Kuzinski

05/15/2020

Step 1

The two expressions inside the absolute value bars can either be equal to each other or they can be opposites of each other. This gives us two equations to solve: Case 1: $3a - 1 = 2a + 4$ Case 2: $3a - 1 = -(2a + 4)$ Show more…

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Solve. $$ |3 a-1|=|2 a+4| $$

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Key Concepts

Linear Equations

Linear equations involve unknowns with a power of one and are solved by isolating the variable through a series of algebraic manipulations. This concept is essential when the cases from an absolute value equation are simplified to yield linear equations.

Absolute Value

This is a measure of distance from zero on the number line, always giving a non-negative result regardless of the sign of the original number. It lays the foundation for equations that involve expressions within absolute value signs.

Case Analysis in Absolute Value Equations

Solving equations that involve absolute values typically requires considering multiple cases. Specifically, if |X| = |Y|, then one must analyze the equations X = Y and X = -Y to cover all possibilities.

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