INEQUALITY WORD PROBLEMS

Solutions to Inequalities Practice

Multiple Select

Select all solutions to

-8(x - 3) - 4x < 108

• -7

• -3

• -6

• -38

Multiple Select

Select ALL 3 that are true solutions:
$$-n+5n\le6n+4$$  

• -2

• -4

• -1

• 5

• -8

Multiple Select

Select all the correct answers that are possible solutions.

-3(x +2) -3x < 2x + 18

• -1

• -4

• 1

• 0

• -3

Multiple Choice

• A

• B

• C

• D

TRANSLATING INQUALITIES

Categorize

Options (20)

$$x<3$$  

$$x>3$$  

$$x\le3$$  

$$x\ge3$$  

in under

fewer than

smaller than

is below

more than

exceeds

is over

is larger than

is higher

is at most

is not greater than

does not exceed

has maximum value

is no more than

is at least

minimum

Organize these options into the right categories USING YOUR NOTES

less than

greater than

less than or equal to

greater than or equal to

Multiple Choice

To order from the kids menu a person must be no more than 12 years old.

• x > 12
• x < 12
• x ≥ 12
• x  ≤ 12

Multiple Choice

Write an inequality for this situation:
You must be at least 18 years old to join the military.

• x > 18
• x < 18
• x ≥ 18
• x ≤ 18

Multiple Choice

Find the inequality that matches the sentence

7 is greater than x

• 7 > x

• 7 < x

• 7 = x

• $$7\ge x$$  

Multiple Choice

Match the inequality to the sentence below.

14 is greater than t

• $$14<t$$

• $$t\le14$$

• $$14\ge t$$

• $$t<14$$

Multiple Choice

Match the inequality to the sentence below.

The sum of 7 and x is less than or equal to -20

• $$7x\le-20$$

• $$7-x\le-20$$

• $$7\ +\ x\le-20$$

• $$7\ +\ x\ =\ -20$$

Multiple Choice

Match the sentence below to the correct inequality.

Eight subtracted from t is greater than 29

• $$8\ -\ t\ >29$$

• $$t\ -\ 8\ >29$$

• $$8\ -\ t\ \le29$$

• $$t\ -\ 8\ \ge29$$

Multiple Choice

Match the sentence to the correct inequality.

The product of -6 and x is greater than or equal to 24

• $$\frac{-6}{x}\ge24$$

• $$-6\ +\ x\ \ge24$$

• $$24\ge-6x$$

• $$-6x\ge24$$

Multiple Choice

Match the sentence to  the correct inequality

The sum of a number times 3 and 15 is less than or equal to 32

• $$3\left(x\ +\ 15\right)\le32$$

• 3 ( x + 15) > 32

• $$3x\ +\ 15\ <32$$

• $$3x\ +15\ \le32$$

Multiple Choice

Match the sentence to the correct inequality

Two times the sum of a number and 28 is at least 21

• $$2\left(x\ +\ 28\right)\ \ge21$$

• $$2x\ +\ 28\ \ge21$$

• 2x + 28 $$>$$ 21

• 2 ( x + 28) < 21

Multiple Choice

Match the sentence to the correct inequality.

Twice the difference of a number and 10 is less than 30

• 2 x + 10 = 30

• 2 ( x-10) < 30

• 2x - 10 < 30

• 2 ( x - 10) $$\le$$ 30

Multiple Choice

Match the scenario to the correct inequality


It takes no less than two hours for Sharika's hair to dry
Use S to represent the amount of hours it takes for her hair to dry

• S $$\ge$$   2 
  

• S < 2

• S > 2

Multiple Choice

Match the scenario to the correct inequality

The distance from my mother to the remote control is less than 10 feet.

Use d to represent the distance in feet to the remote control

• $$d\ =10$$  

• $$d\le10$$  

• $$d\ \ge10$$  

• d < 10

Multiple Choice

Match the scenario to the correct inequality.

To get the 25% discount, a shopper must spend at least $100.

(use d to represent the spending of a shopper who gets the discount)

• $$d\ \le100$$

• $$d\ \ge100$$

• d > 100

• d = 100

Multiple Choice

Four times the sum of a number m and 5 is no less than 48

• $$4\left(m\ +\ 5\right)\ \ge48$$
  

• $$4\left(m\ +\ 5\right)\ \le48$$

• $$4\ \times\ m\ +\ 5\ \ge48$$

• $$4\ \times m\ +\ 5\le48$$

Multiple Choice

The quotient of y and a number 5 plus 3 is no more than 38

• $$\frac{y}{5}\ +\ 5\ <38$$

• $$\frac{y}{5}\ +\ 3\ >38$$

• $$\frac{y}{5}\ +\ 3\ \ge38$$

• $$\frac{y}{5}\ +\ 3\ \le38$$

Multiple Choice

Match the sentence to the correct inequality

Two times the quantity of a number increased by 28 is at least 21

• $$2\left(x\ +\ 28\right)\ \ge21$$

• $$2x\ +\ 28\ \ge21$$

• 2x + 28 $$>$$ 21

• 2 ( x + 28) < 21

Multiple Choice

Melissa wants to spend no more than $300 on school clothes. She spends $75 on a coat and then wants to buy some sweaters that are on special for $10 each. Write an inequality to show how many sweaters Melissa can buy. DO NOT SOLVE

• 75x-10 ≥ 300
• 75+10 ≤ 300x
• 10x ≥ 300
• 75+10x ≤ 300

Multiple Choice

Joan needed $100 to buy a graphing calculator for her math class. Her neighbor will pay her $5 per hour to babysit and her Father gave her $10 for mowing the lawn. Which inequality represents the minimum amount of hours she will need to babysit in order for her to buy her calculator?

• 5x + 10 ≥ 100
• 5x - 100 ≥ 10
• 10x + 5 ≤ 100
• 5x + 10 > 100

Multiple Choice

The dance committee hired a DJ for the fall dance. The DJ charges $125 per hour in addition to $55 for an assistant. The committee wants to keep the total cost under $600. Which inequality represents the maximum amount of hours the DJ will play at the dance?

• 125x + 55 ≤ 600
• 125x + 55 ≥ 600
• 125x + 55 > 600
• 125x + 55 < 600

Multiple Choice

You downloaded a video game to your computer. You have a 60 minute free trial of the game. It takes 5 minutes to set up the game and 7 minutes to play each level. Write an inequality to show how many levels you can play. DO NOT SOLVE

• 5x-7 ≥ 60
• 7x+5 ≤ 60
• 7+5 ≤ 60x
• 7x-5 ≥ 60

Multiple Choice

Daniel can spend no more than $40 at the fair. If admission into the fair is $10 and the rides cost $1.50 each, which inequality represents the greatest number of rides Daniel can go on?

• 10x + 1.50 ≥ 40
• 1.50x + 10 ≤ 40
• 1.50x + 10 <40
• 10x + 1.50 < 40

Multiple Choice

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. Which inequality represents her situation?

• 200 + 25x ≥ 500
• 500 + 25x ≥ 200
• 500 - 25x ≥ 200
• 500 - 25x ≤ 200