### Home > CCA2 > Chapter C > Lesson C.1.2 > ProblemC-37

C-37.

Solve the following inequalities for $x$. Graph your solutions on a number line.

1. $3x -​ 5 ≤ 7 + 2x$

Treat the inequality sign like an equation, then solve.
$3x − 5 = 7 + 2x$
$x − 5 = 7$
$x = 12$

Check a point to see which side is true.

$x ≤ 12$

1. $|x| - 3 < 7$

Solve for the absolute value of $x$, then make two equations.

$|x| − 3 = 7$
$|x| = 10$

$x = ±10$

Test numbers to determine which region is the solution.

$-10 < x < 10$

1. $5(2 − x) + 6 > 16$

Distribute, then solve for $x$.

$x > 0$

1. $| x + 2 | > 3$

See part (b).