### Home > CC4 > Chapter 11 > Lesson 11.2.1 > Problem 11-53

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

a.

+ 3 < 5 b.

5(2

*x*+ 1) ≥ 30c.

d.

−5 −

*x*> 3 −*x*e.

3

+ 1 = 13 f.

≤ 4

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(2*x* + 1) ≥ 30

5(2*x* + 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 2*x* as Fraction Buster to eliminate the fractions.

2 − 5*x* = 3*x*

Add *x* to both sides.

−5 − *x* + *x* > 3 − *x* + *x*

−5 > 3

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

Subtract 1 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).