Lesson 8.3: solving inequalities

GRADE 7 Module 8 Lesson 3.
Apply Two-Step Inequalities to Solve Problems

Multiple Choice

Jerry has at least 15 model cars. Write an inequality that represents this situation.

• c < 15

• c > 15

• c ≥ 15

• c ≤ 15

© Houghton Mifflin Harcourt Publishing Company

I Can.

I Can write and solve two-step inequalities for

real-world scenarios.

© Houghton Mifflin Harcourt Publishing Company

Step It Out • Task 1 ACTIVITY.

A population study was performed to find the number of deer in two parks. The study

found that twice the number of deer in Maple Park is at least 20 more than the number

of deer in Smith Park. The study found that there are 50 deer in Smith Park.

A.

Write an expression to represent the difference between twice the number of deer

in Maple Park and the number of deer in Smith Park. Use x for the number of deer in

Maple Park.

B.

What do you know is true about this difference?

The difference is ________ than or equal to _____.

​2x - 50( 2 * the number of deer in Smith Park - 50

​greater 20

© Houghton Mifflin Harcourt Publishing Company

Step It Out • Task 1 ACTIVITY.

A population study was performed to find the number of deer in two parks. The study

found that twice the number of deer in Maple Park is at least 20 more than the number

of deer in Smith Park. The study found that there are 50 deer in Smith Park.

C.

Write and solve the inequality to determine the

possible number of deer in Maple Park.

​2x - 50 ≥ 20
add 50 to both sides
2x ≥ 70
Divide both sides by 2
x ≥ 35

© Houghton Mifflin Harcourt Publishing Company

Step It Out • Task 1 ACTIVITY.

A population study was performed to find the number of deer in two parks. The study

found that twice the number of deer in Maple Park is at least 20 more than the number

of deer in Smith Park. The study found that there are 50 deer in Smith Park.

D.

Graph the solution of the inequality. Do all the values make sense? Explain.

E.

What does the solution of the inequality represent in the problem?

In ________ Park, there are ________ deer.

​Maple at least 35

Math Response

Rosina and Asia collect stamps. The number of stamps Rosina has is 7 more than 3 times the number of stamps Asia has. Rosina has less than 85 stamps. How many stamps can Asia have?

Type answer here

Correct Answer: x<26

Deg^°

Rad

Math Response

Solve the inequality: –3b – 2 ≤ 13.

Type answer here

Correct Answer: b\ge-5

Deg^°

Rad

Open Ended

Monica and Lucy are participating in a scavenger hunt. The number of items Monica found is 7 more than 1/2 the number of items Lucy found. The number of items Monica found is at least 17. Write and solve the inequality to find what you know about the number of items Lucy found.

​

Monica and Lucy are participating in a scavenger hunt. The number of items Monica found is 7 more than 1/2 the number of items Lucy found. The number of items Monica found is at least 17.
Graph the solution x ≥ 20

Math Response

Solve the inequality –7m + 4 < –45.

Type answer here

Correct Answer: m>7

Deg^°

Rad

Math Response

The number of students using the cafeteria's healthy lunch line can be found by solving the inequality 1/2s - 51 ≤ 20.

How many students use this lunch line?

Type answer here

Correct Answer: s\le142

Deg^°

Rad

Math Response

Raj has a sticker collection with 35 stickers. He wants to have at least 100 stickers in his collection. If stickers come in packs of 12, how many packs must he buy to reach his goal?

Type answer here

Correct Answer: s\ge6

Deg^°

Rad