3.06 Absolute value equations and inequalities

Interactive practice questions

How many solutions will the equation $\left|x\right|=a$|x|=a, where $a$a is a positive number, always have?

Easy

< 1min

Solve the equation $\left|x\right|=8$|x|=8.

Write both solutions as equations on the same line separated by a comma.

Easy

< 1min

Solve the equation $9\left|x\right|=4$9|x|=4.

Write both solutions as equations on the same line separated by a comma.

Easy

1min

What is/are the solution(s) to the absolute value equation $\left|x\right|=-8$|x|=−8?

Easy

< 1min

Solve graphically or algebraically equations of the type |ax + b| = c (c ⩾ 0) and |ax + b| = |cx + d|.

Solve graphically or algebraically inequalities of the type |ax + b| > c (c ⩾ 0), |ax + b| ⩽ c (c > 0) and |ax + b| ⩽ |cx + d|.