### Home > INT1 > Chapter Ch11 > Lesson 11.2.1 > Problem 11-53

Solve the inequalities and equations below. Represent your solutions for each inequality on a number line.

Isolate the absolute value by subtracting

from both sides. Change the inequality into an equation and solve for

.Graph both values of

on the number line, which divides the line into three regions.

Substitute a value from each region into the original inequality.

Whichever regions make the inequality true are the solutions.

Change to an equation and solve for

.Graph

on a number line.

Then check values from both regions to find the solution.

Don't forget to represent your solution with a number line!

Multiply both sides by

as Fraction Buster to eliminate the fractions.

Add

*x*to both sides.

Is this statement true? If so, then*x*can be any real number. If not, then there is no real solution.

Subtract

from both sides. Then divide by three.

This will isolate the square root. Look inside to determine the solution.

See the help for part (a).