### Home > CCA > Chapter 11 > Lesson 11.2.1 > Problem11-38

11-38.
1. Solve the inequalities and equations below, if possible. Represent your solution on a number line. Homework Help ✎

1. + 3 < 5

2. 5(2x + 1) ≥ 30

3. =

4. −5 − x > 3 − x

5. + 1 = 13

6. ≤ 4

See problems 11-21 and 11-30 for additional help.

Isolate the absolute value by subtracting 3 from both sides.
|x| + 3 < 5
|x| + 3 − 3 < 5 − 3
|x| < 2

Change the inequality into an equation and solve for x.
|x| < 2
|x| = 2
x = {2, −2}

Graph both values of x 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 x.
5(2x + 1) ≥ 30
5(2x + 1) = 30
x = 2.5

Graph x on a number line. Then check values from both regions to find the solution.

x ≥ 2.5
Don't forget to represent your solution with a number line!

Multiply both sides by 2x as Fraction Buster to eliminate the fractions.

$\left(\frac{1}{x}\right)2x-\left(\frac{5}{2}\right)2x=\left(\frac{3}{2}\right)2x$

2 − 5x = 3x

$\textit{x}=\frac{1}{4}$