**Written Homework 9:**50. $\left| \frac{1}{2}x + \frac{3}{2} \right| = \left| \frac{3}{2}x - \frac{7}{2} \right|$In this equation, we are dealing with absolute value expressions. To solve it, you should consider both cases where the expressions inside the absolute value brackets are equal and where they have equal magnitudes but opposite signs. Proceed by setting up the equations:1. Case 1: $\frac{1}{2}x + \frac{3}{2} = \frac{3}{2}x - \frac{7}{2}$2. Case 2: $\frac{1}{2}x + \frac{3}{2} = -\left(\frac{3}{2}x - \frac{7}{2}\right)$Solve each equation separately to find the value(s) of $x$.

Answered: Written Homewonk 9: 3. 3

Math

Algebra

Written Homewonk 9: 3. 3

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

**Written Homework 9:**

50. $\left| \frac{1}{2}x + \frac{3}{2} \right| = \left| \frac{3}{2}x - \frac{7}{2} \right|$

In this equation, we are dealing with absolute value expressions. To solve it, you should consider both cases where the expressions inside the absolute value brackets are equal and where they have equal magnitudes but opposite signs.

Proceed by setting up the equations:

1. Case 1: $\frac{1}{2}x + \frac{3}{2} = \frac{3}{2}x - \frac{7}{2}$
2. Case 2: $\frac{1}{2}x + \frac{3}{2} = -\left(\frac{3}{2}x - \frac{7}{2}\right)$

Solve each equation separately to find the value(s) of $x$.

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