Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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**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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Transcribed Image Text:**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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