Solving One and Two Step Inequalities and Word Problems

| x + 3 | ≤ 2

• No Solution

• x ≤ -1

• -5 ≤ x and x ≤ -1

• 1 ≤ x and x ≤ 5

• no solution
• x > 2 or x < -22
• -22 < x < 2
• all real numbers

Solve for r.

• r ≥ -38 and r ≤ 32

• r > -38 and r < 32

• r ≥ -38 or r ≤ 32

• r > -38 or r < 32

• A
• B
• C
• D

Solve.
-5|x - 4| > -20

• x < 8 and x > 0

• x > 8 or x < 0

• all real numbers

• no solution

Solve.
-5|x - 4| > 20

• x < 8 and x > 0

• x > 8 or x < 0

• all real numbers

• no solution

Solve.
-5|x - 4| < 20

• x < 8 and x > 0

• x > 8 or x < 0

• all real numbers

• no solution

The radius of the gears produced at a factory must be 6 inches in length with a tolerance of 0.1 inches. The gears with radius beyond the tolerated lengths will be thrown away. Which of the following inequalities can be used to assess which gears are eligible? (x is the length of the radius)

• |x – 6| ≤ 0.1

• |x – 6| ≥ 0.1

• |x – 0.1| ≤ 6

• |x – 0.1| ≥ 6

The street built in the city must be 25 feet in width with a tolerance of 0.5 feet. Streets that are not within the tolerated widths must be repaired. Which of the following inequalities can be used to assess which streets are within tolerance? (W is the width of the street) .

• |W - 25| ≤ .5

• |W - .5| ≤ 25

• |W - 25| ≥ .5

• |W - .5| ≥ 25

Which compound inequality involves <, ≤ when solving absolute value inequalities?

• and

• or