SOLVING INEQUALITIES USING MULTIPLICATION OR DIVISION WORKSHEET

Solve the inequality.

1)  4x < 4                   Solution

2)  -2x ≤ 2          Solution

3)  -5x > 15          Solution

4)  x/-3 ≥ 1          Solution

5)  x/-2 > 5/2          Solution

6)  x/4 ≤ 3/8          Solution

Solve the inequality. Graph the solution.

1)  3n > 18          Solution

2)  c/4 ≤ -9          Solution

3)  1.2m < 12          Solution

4)  -14 > x ÷ 2          Solution

5)  w/5 ≥ -2.6          Solution

6)  5 < 2.5k          Solution

7)  4x ≤ -3/2          Solution

8)  2.6y ≤ -10.4          Solution

9)  10.2 > b/3.4          Solution

Problem 10 :

The tallest person who ever lived was approximately 8 feet 11 inches tall.

a. Write an inequality that represents the heights of every other person who has ever lived.

b. Is 9 feet a solution of the inequality? Explain.

Solution

Problem 11 :

The winner of a weight-lifting competition bench-pressed 400 pounds. The other competitors all bench-pressed at least 23 pounds less.

a. Write an inequality that represents the weights that the other competitors bench-pressed.

b. Was one of the other competitors able to bench-press 379 pounds? Explain.

Solution

Problem 12 :

A circuit overloads at 1800 watts of electricity. You plug a microwave oven that uses 1100 watts of electricity into the circuit.

a. Write and solve an inequality that represents how many watts you can add to the circuit without overloading the circuit.

b. In addition to the microwave oven, which of the following appliances can you plug into the circuit at the same time without overloading the circuit

Solution

Answer Key

1)  n > 6

2)  c ≤ -36

3)  m < 10

4)  -28 > x

5)  w ≥ -13

6)  k > 2

7)  x ≤ -3/8

8)  y ≤ -4

9)  b < 34.68

10) a) h < 107

b) 9 feet is not the solution.

11) a) x ≤ 377

b) 379 ≤ 377

12) The circuit will not overload because the total wattage is less than 1800 watts.

Problem 1 :

Amanda rented a bike from Shawna's Bikes. They charged her $2 per hour, plus a $10 fee. Amanda paid less than $27.

a) Write an inequality to represent the situation. Be sure to define your variable.

b) Solve the inequality to find the maximum number of hours Amanda rented the bike.

Solution

Problem 2 :

You need to buy some pencils and an eraser. You can spend no more than $5. The eraser costs $1 and the pencils cost $0.25 each.

a) Write an inequality to represent the situation. Be sure to define your variable.

b) Solve the inequality to find the maximum number of pencils you can buy.

Solution

Problem 3 :

Mark's Canoes rents canoes for $20 plus $35 per hour. You do not want to spend more than $150. For how many hours can you afford to rent the canoe?

a) Write an inequality to represent the situation. Be sure to define your variable.

b) Solve the inequality and answer the question.

Solution

Problem 4 :

For a field trip 18 students rode in cars and the rest filled five buses. How many students were in each bus if no more than 250 students went on the trip?

a) Write an inequality to represent the situation. Be sure to define your variable.

b) Solve the inequality and answer the question.

Solution

Problem 5 :

Charles is saving $5 each week. He earns an extra $15 by mowing his neighbor's lawn. How many weeks will he need to save in order to have at least $75?

a) Write an inequality to represent the situation. Be sure to define your variable.

b) Solve the inequality and answer the question.

Solution

Problem 6 :

Write an inequality that represents the missing dimension x. The area is less than 42 square meters.

Solution

Problem 7 :

The area is greater than or equal to 8 square feet.

Solution

Problem 8 :

The area is less than 18 square centimeters.

Solution

Problem 9 :

The area is greater than 12 square inches.

Solution

Problem 10 :

You order the hardcover book shown from a website that offers free shipping on orders of $25 or more. Write and solve an inequality that represents how much more you must spend to get free shipping.

Solution

Problem 11 :

You are riding a train. Your carry-on bag can weigh no more than 50 pounds. Your bag weighs 38 pounds.

a. Write and solve an inequality that represents how much weight you can add to your bag.

b. Can you add both a 9-pound laptop and a 5-pound pair of boots to your bag without going over the weight limit? Explain.

Solution