Solving/Interpreting Linear Inequalities in One Variable Absolute Value

| 12 + w | ≥ -5

• No Solution

• All Real Numbers

• w ≤ -17  or  w ≥ -7

• -17 ≤ w ≤ -7

Solve.

3|2d + 9| + 13 > 10

• d > 5 or d < -1

• d < -4 or d > 5

• No Solution

• All real numbers

Solve the inequality |3x - 2| < 10.

• -8/3 < x < 4

• -10 < x < 10

• -5 < x < 5

• -8/3 < x < 4

• - 1/3 < n or n > 5/3
• -1/3 < n < 5/3
• 1/3 < n < 5/3
• n < -5/3 or n > 1/3

• no solution
• a> -1/6 or a< -5/6
• a>1/2 or a< -3/2
• all real numbers

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 – 0.5| ≥ 25

• |W – 0.5| ≤ 25

• |W – 25| ≥ 0.5

• |W – 25| ≤ 0.5

• n > 1 or n < -7

• n > -1 or n < -7

• -7 < n < -1

• no solution

Solve for r.

• r ≥ -38 and r ≤ 32

• r > -38 and r < 32

• r ≥ -38 or r ≤ 32

• r > -38 or r < 32

Solve.
|y - 1| ≤ 6

• -7 ≤ y ≤ 5

• y ≤ -7 or y ≥ 5

• -5 ≤ y ≤ 7

• y ≤ -5 or y ≥ 7

An absolute value inequality is

• an inequality that contains an absolute value expression

• impossible to solve

• an equation that contains an absolute value expression

• always going to have two solutions