Example

Try It: Solving 3x44=83|x - 4| - 4 = 8 and 2x5+3=92|x - 5| + 3 = 9

To practice isolating absolute value expressions with a coefficient, solve the equations 3x44=83|x - 4| - 4 = 8 and 2x5+3=92|x - 5| + 3 = 9. For the first equation, add 44 to both sides to get 3x4=123|x - 4| = 12, then divide by 33 to find x4=4|x - 4| = 4. The equivalent equations are x4=4x - 4 = -4 or x4=4x - 4 = 4, which solve to x=0x = 0 or x=8x = 8. For the second equation, subtract 33 from both sides to obtain 2x5=62|x - 5| = 6, then divide by 22 to yield x5=3|x - 5| = 3. The equivalent equations x5=3x - 5 = -3 or x5=3x - 5 = 3 solve to x=2x = 2 or x=8x = 8.

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Updated 2026-05-02

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