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

11-53.
  1. Solve the inequalities and equations below. Represent your solutions for each inequality on a number line. Homework Help ✎

  2. a.

    + 3 < 5

    b.

    5(2x + 1) ≥ 30

    c.

    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(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).