Mastering Absolute Value Inequalities and Graphing

A store sells a jacket for $50. If the price can vary by at most $10, what is the range of prices for the jacket? Graph the inequality.

• $40 to $60

• $50 to $70

• $45 to $55

• $30 to $50

A temperature must stay within 5 degrees of 70°F for a party to be comfortable. Write and solve the absolute value inequality to find the acceptable temperature range.

• The acceptable temperature range is 65°F to 75°F.

• 55°F to 65°F

• 60°F to 70°F

• 70°F to 80°F

A car's speed must not exceed 60 mph, but it can also be 5 mph slower. Write an absolute value inequality to represent this situation and graph it.

• |x - 50| ≤ 10

• |x - 55| ≤ 5

• |x + 60| ≤ 5

• |x - 60| ≤ 5

A student scored 85 on a test, and the teacher allows scores to vary by 7 points for a passing grade. What is the range of passing scores? Solve the inequality and graph it.

• 75 to 95

• 70 to 100

• The range of passing scores is 78 to 92.

• 80 to 90

A basketball player wants to maintain a weight that is within 3 pounds of 180 pounds. Write the absolute value inequality and determine the range of acceptable weights.

• The range of acceptable weights is (178, 182).

• The range of acceptable weights is (177, 183).

• The range of acceptable weights is (175, 185).

• The range of acceptable weights is (180, 186).

A delivery truck must keep its load weight within 200 pounds of 1,000 pounds. Write the absolute value inequality and graph the solution set.

• |x - 800| ≤ 200

• |x - 1200| ≤ 200

• |x - 1000| ≤ 200

• |x + 1000| ≤ 200

A runner's pace should be within 2 minutes of 8 minutes per mile. Write the absolute value inequality and find the range of acceptable paces.

• 6 to 10 minutes per mile

• 4 to 8 minutes per mile

• 10 to 14 minutes per mile

• 8 to 12 minutes per mile

A school wants to keep the number of students in a classroom within 5 of 30. Write the absolute value inequality and graph the solution.

• |x - 25| < 5

• |x - 30| < 5

• |x - 30| > 5

• |x + 30| < 5

A plant needs to be watered when the soil moisture level is within 4 units of 10. Write the absolute value inequality and determine the acceptable moisture levels.

• The acceptable moisture levels are between 0 and 4.

• The acceptable moisture levels are between 8 and 12.

• The acceptable moisture levels are between 5 and 15.

• The acceptable moisture levels are between 6 and 14.

A family wants to keep their monthly expenses within $100 of their budget of $2,000. Write the absolute value inequality and find the range of acceptable expenses.

• The range of acceptable expenses is between $2,100 and $2,300.

• The range of acceptable expenses is between $1900 and $2100.

• The range of acceptable expenses is between $1,950 and $2,050.

• The range of acceptable expenses is between $1,800 and $2,200.