Absolute Value Equations and Inequalities

Question

Solve the compound inequality −1 < −3x − 3 < 15 and write the solution using algebraic notation, then line graph your solution.

Answer 1

−1 < −3x − 3 < 15

Just like a regular equation, solve for the x. First, add 3 to all sides:

2 < -3x < 18

Now divide all sides by -3. When you multiply or divide an inequality by a negative number, you flip the inequality symbols, in this case, flip from < to >:

-2/3 > x > -6

< ------o=========o--------->

-6 x -2/3