SOLVING INEQUALITIES WITH ONE VARIABLE WORKSHEET

Solve each inequality.

Problem 1 :

4x - 1 ≥ 7

Solution

Problem 2 :

2(x – 5) ≤ 8

Solution

Problem 3 :

3 – 2x < x + 6

Solution

Problem 4 :

1/2x > 5

Solution

Problem 5 :

3(x + 4) > 12

Solution

Problem 6 :

2x – 7 ≤ 5 – 4x

Solution

Problem 7 :

3x + 2 < 11

Solution

Problem 8 :

4(x – 6) ≥ 20

Solution

Problem 9 :

1/4x < 2

Solution

Problem 10 :

12 – 3x > 2x + 1

Solution

Problem 11 :

(x – 5)/7 ≤ -3

Solution

Problem 12 :

3(5 – x) ≥ 7x - 1

Solution

Problem 13 :

3y – (2y + 2) ≤ 7

Solution

Problem 14 :

(m + 2)/5 < 2m/3

Solution

Problem 15 :

(m – 2)/3 ≥ (2m + 1)/7

Solution

Problem 1 :

Jacob weights more than 50 pounds more than his younger brother, Jared. Jared weighs 46 pounds.

Solution

Problem 2 :

Analice is 16 years old. If you add together Analice's age and her cousin, Emily's age together you will get more than 31 years.

Solution

Problem 3 :

Bracelets cost $3 each. Rachel can spend no more than $20. How many bracelets can he buy ?

Solution

Problem 4 :

Max earns $9 per hour. This week he is hopping to earn at least $200. How many hours would he need to work ?

Solution

Problem 5 :

James has $32. He starts shoveling driveways and earns $7 per driveway. He needs at least $75 to buy a skateboard he wants. How many driveways does he need to shovel ?

Solution

Problem 6 :

The seventh grade class is putting on a variety show to raise money. It cost $700 to rent the banquet hall that they are going to use. If they charge $15 for each ticket, how many tickets do they need to sell in order to raise at least $1000?

Solution

Problem 7 :

Kevin has $25. MP3 downloads cost $0.75 each. How many songs can he download and still have $13 left to spend?

Solution

Problem 8 :

Triniti had $500 in a saving account at the beginning of the summer. She wants to have at least $200 in the account by the end of the summer. She withdraws $25 each week for food, clothes, and movie tickets.

Solution

Problem 9 :

The graphs show the height restrictions h (in inches) for two rides at an amusement park. Write an inequality that represents the height restriction of each ride.

Solution

Problem 10 :

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 11 :

The graph represents the known melting points of all metallic elements (in degrees Celsius).

a. Write an inequality represented by the graph.

b. Is it possible for a metallic element to have a melting point of −38.87°C? Explain.

Solution

Solve the inequalities and represent the possible values of the variable on a number line.

Problem 1 :

6 > z - 2

Solution

Problem 2 :

g + 7 < -12

Solution

Problem 3 :

d – 5 < 7

Solution

Problem 4 :

15 > k + 2

Solution

Problem 5 :

1 + x > -16

Solution

Problem 6 :

y + 8 < -9

Solution

Problem 7 :

8 ≤ 8 + r

Solution

Problem 8 :

w + 8 ≥ 11

Solution

Problem 9 :

The NASA Solar Probe can withstand temperatures up to and including 2600°F. Write and graph an inequality that represents the temperatures the probe can withstand.

Solution

Problem 10 :

Describe and correct the error in graphing the inequality.

Solution

Problem 11 :

Describe and correct the error in graphing the inequality.

Solution

Problem 12 :

Each day at lunchtime, at least 53 people buy food from a food truck. Write an inequality that represents this situation.

Solution

Problem 13 :

A subway ride for a student costs $1.25. A monthly pass costs $35.

a. Write an inequality that represents the number of times you must ride the subway for the monthly pass to be a better deal.

b. You ride the subway about 45 times per month. Should you buy the monthly pass? Explain.

Solution

Problem 14 :

Consider the inequality b > − 2.

a. Describe the values of b that are solutions of the inequality.

b. Describe the values of b that are not solutions of the inequality. Write an inequality for these values.

c. What do all the values in parts (a) and (b) represent? Is this true for any inequality?

Solution

Problem 15 :

A postal service says that a rectangular package can have a maximum combined length and girth of 108 inches. The girth of a package is the distance around the perimeter of a face that does not include the length.

a. Write an inequality that represents the allowable dimensions for the package.

b. Find three different sets of allowable dimensions that are reasonable for the package. Find the volume of each package.

Solution

Answer Key

1) z < 8

2) g < -19

3) d < 12

4) k < 13

5) x > -17

6) y < -17

7) r ≥ 0

8) w ≥ 3

9)

10) By observing the graph, the values of x is greater than or equal to 1. The circle should be closed circle.

11) By observing the graph, the values of x is lesser than to 1. The circle should be open circle.

12) x ≥ 53 (at least)

13)  a) the minimum number of times the monthly pass t be used is 28.

b) Since the amount what we receive is greater than 35, we should purchase monthly pass to reduce expenses.

14) a) The values of b should be greater than -2.

b) The values of b should be lesser than -2 including -2.

c) These values represent all real numbers. This is true for any inequality because every real number is either a solution or it is not.

15) a) l + 2w + 2h ≤ 108

b) 4800 cubic inches, 4500 cubic inches, 3600 cubic inches