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Section 2.14 : Absolute Value Equations

For problems 1 – 10 solve each of the equation.

1. \(\left| {2x + 9} \right| = 7\)
2. \(\left| {5w - 2} \right| = 3\)
3. \(\left| {6 - 7t} \right| = 10\)
4. \(\displaystyle 2 = \left| {\frac{1}{4}m - \frac{1}{3}} \right|\)
5. \(\left| {8u + 9} \right| = 9\)
6. \(\left| {x + 3} \right| = 4x + 1\)
7. \(\left| {2z - 7} \right| = 3z - 10\)
8. \(\left| {3y + 9} \right| = 10 - y\)
9. \(\left| {6w + 12} \right| = 1 + w\)
10. \(\left| {8x + 3} \right| = 0\)

For problems 11 – 13 find all the real valued solutions to the equation.

1. \(\left| {{x^2} + 1} \right| = - 4\)
2. \(\left| {{u^2} - 7u} \right| = 12\)
3. \(\left| {{z^2} - 6} \right| = z\)