Chapter 1, Equations and Inequalities - 1.7 Solve Absolute Value Equations and Inequalities - 1.7 Exercises - Skill Practice - Page 55: 34

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Since the value inside the absolute value can be positive or negative and get the same number, we must consider both options. Doing this, we find: $$ 3x-4=\pm x \\ x=1\quad \mathrm{or}\quad \:x=2$$ These are not extraneous solutions.