Algebra I: 1,001 Practice Problems For Dummies

      711.           x = −1 or x = −7

The absolute value equation 3|x + 4| − 2 = 7 needs to be rewritten before applying the equivalency involving linear equations.

First add 2 to each side to isolate the absolute value expression on the left; you get 3|x + 4| = 9. Next divide each side of the equation by 3 to get |x + 4| = 3.

The absolute value equation is equivalent to the two linear equations x + 4 = 3 and x + 4 = −3.

Adding −4 to each side of the two equations, you get x = −1 and x = −7, respectively.

      712.          

The absolute value equation is equivalent to the two linear equations −3x = 4 and −3x = −4. Dividing each side of the two equations by −3, you get x = or x = , respectively.

      713.           x = −9 or x = 6

The absolute value equation is equivalent to the two linear equations −2x − 3 = 15 and −2x − 3 = −15.

Solving the first equation, you add 3 to each side of the equation to get −2x = 18. Dividing each side of the equation by −2, you have x = −9.

Solving the second equation, you add 3 to each side of the equation to get −2x = −12. Dividing each side by −2, you have x = 6.

      714.           No solution

The absolute value equation |3x − 2| + 4 = 1 needs ...