Inequalities Word Problems Guided Practice Lesson

​TIP! Keep your Inequality anchor charts in view and use them throughout this lesson. They have the answers and illustrate how to answer all your questions.

Categorize

Options (14)

fewer than

at most

at least

a maximum of

a minimum of

more than

up to and including

no more than

longer than

smaller than

under

bigger than

no less than

no fewer than

Math the phrase with the inequality symbol. Use your anchor chart.

Less than

Greater than

Less than or equal to

Greater than or equal to

Multiple Choice

Select the inequality shown

• x > -2

• x ≥ -2

• x < -2

• x ≤ -2

Multiple Select

Select the answer choices that are part of the solution set of x ≥ -2 (Select all that apply)

• -4

• -2

• 0

• 10

• 1245

Multiple Select

Which of the following are part of the solution set of x < -4?

• 4

• -2

• -4

• -5

• -6

Multiple Choice

$$x\ge7$$  

• shade to the LEFT

• shade to the RIGHT

Multiple Choice

$$x>-2$$  

• shade to the LEFT

• shade to the RIGHT

Multiple Choice

The next town is at least 40 miles away. (Use your anchor chart to find which inequality symbol to use for the term "at least"

• $$x<40$$  

• $$x\le40$$  

• $$x>40$$  

• $$x\ge40$$  

Multiple Choice

You can spend at most $5.00. (Use anchor chart to match the inequality and the term at most)

• $$x\ge5$$  

• $$x\le5$$  

• $$x>5$$  

• $$x<5$$  

Multiple Choice

My math grade is greater than 70.

• $$x\le70$$  

• $$x<70$$  

• $$x>70$$  

• $$x\ge70$$  

Multiple Choice

Fewer than 30 people were on the trip.

• $$x>30$$  

• $$x\ge30$$  

• $$x<30$$  

• $$x\le30$$  

Multiple Choice

• A

• B

• C

• D

Multiple Choice

• A

• B

• C

• D

Multiple Choice

Which inequality represents the real-world situation below?

“Doctors say you should exercise at least 30 minutes every day.”

• x $$<$$ 30

• x $$>$$ 30

• x $$\le$$ 30

• x $$\ge$$ 30

Multiple Choice

You start a dog walking business. Each dog earns you $8.

Which of the following inequalities could help you find all the possible values of d, the amount of dogs you will need to walk, to have more than $32?

• $$8x\ >32$$

  
  

• 
  

  $$8x\ \ge32$$

• $$8x\ <32$$

• $$8x\ \le32$$

Multiple Choice

Which sentence represents m > 41?

• Mary’s points, m, totaled more than 41
• Calvin ran no less than 41 miles, m
• The temperature, m, was less than 41°F
• The magazines’ cost, m, was not more than $41.

Multiple Choice

A new tree you just planted will grow to be at most 35 feet tall. If it is currently 6 feet tall.

Which of the following inequalities could be used to find all all the possible values of how many more feet, f, will it grow?

• 6 + x ≥ 35

• 6 + x > 35

• 6 + x < 35

• 6 + x ≤ 35

Multiple Choice

Julie had twins that weighed less than 16 pounds together. If each twin weighed the same amount, which of the following inequalities could be used to find all the possible values of w, the amount each twin weighs? Which displays the correct solution?

• 2x ≤ 16

  Solution: x ≤ 8

• 2x > 16

  Solution: x > 8

• 2x ≥ 16

  Solution: x ≥ 8

• 2x < 16

  Solution: x < 8

Draw

Julie had twins that weighed less than 16 pounds together.

Since we found that 2x < 16 represented the solution and x < 8 is the solution. Graph the solution.

Multiple Choice

The school PTA would like to raise a minimum of $3,000 in the cookie dough fundraiser. If each container to cookie dough costs $15, which inequality can be used to find how many containers of cookie dough the school needs to sell?

• 15 + 5 ≥ 3000

• 15x ≤ 3000

• 15 + x ≤ 3000

• 15x ≥ 3000

Multiple Choice

Monica wants to spend at most $40 at the county fair. Entrance to the fair costs $15. She can spend d dollars on other things at the fair. Which phrase indicates what inequality symbol you should use?

• costs

• $40

• spend

• at most

Multiple Choice

The phrase "at most" indicates you will use which inequality symbol? (Use your anchor chart to confirm)

• <

• >

• ≤

• ≥

Multiple Choice

Monica wants to spend at most $40 at the county fair. Entrance to the fair costs $15. She can spend d dollars on other things at the fair. Which inequality can be used to find the possible values of d?

• d − 15 > 40

• d − 15 < 40

• d + 15 ≥ 40

• d + 15 ≤ 40

Multiple Choice

Monica wants to spend at most $40 at the county fair. Entrance to the fair costs $15. She can spend d dollars on other things at the fair. Which inequality can be used to find the possible values of d?

Since the situation can be represented with the inequality d + 15 ≤ 40, which answer choice correctly displays how to solve for "d".

• d + 15 ≤ 40

  -15

  d ≤ 40

• d + 15 ≤ 40

  -15 -15

  d ≤ 25

• d + 15 ≤ 40

  +15 +15

  d + 30 ≤ 55

• d + 15 ≤ 40

  -40 -40

  d -35 ≤ 0

Multiple Choice

x - 62 = 123
How should you show your work to isolate the variable and solve the equation?

• Add 62 to each side. 
• Subtract 62 from each side.
• Multiply each side by 62.
• Add 123 to each side.

Multiple Choice

x - 62 < 123
+62 +62

What is the solution

• x < 61

• x < 185

• x > 185

• x > 61

Multiple Choice

Mrs. Scott decided that she would spend no more than $120 to buy birthday presents for her triplets. Which inequality can be used to determine the maximum Mrs. Scott can spend on each child?

• 3x > 120

• 3x ≤ 120

• x + 3 ≤ 120

• x + 3 > 120

Categorize

Options (14)

fewer than

at most

at least

a maximum of

a minimum of

more than

up to and including

no more than

longer than

smaller than

under

bigger than

no less than

no fewer than

Math the phrase with the inequality symbol. Use your anchor chart.

Less than

Greater than

Less than or equal to

Greater than or equal to