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Home > CCA > Chapter 11 > Lesson 11.2.1 > Problem 11-38

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.

2 − 5x = 3x

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).