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6-8 Grade 7 Unit 6 Lesson 14

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Lesson 14

14.1 Warm-up 14.2 Activity 14.3 Activity Student Lesson Summary Glossary

Unit 6, Lesson 14

Finding Solutions to Inequalities in Context

Grade 7

14.1

Warm-up

Solutions to Equations and Solutions to Inequalities

Solve
Find 2 values of that make this inequality true:
Solve
Find 2 values of that make this inequality true:

Are You Ready for More?

14.2

Activity

Earning Money for Soccer Stuff

Andre has a summer job selling magazine subscriptions. He earns $25 plus $3 for every subscription he sells. Andre hopes to earn enough money to buy a new pair of soccer cleats.
1. Write an expression for the amount of money that Andre earns. Use to represent the number of magazine subscriptions he sells.
2. The cleats that Andre wants cost $68. Write and solve an equation to find out how many magazine subscriptions Andre needs to sell to buy the cleats.
3. If Andre sold 16 magazine subscriptions this week, would he reach his goal? Explain your reasoning.
4. What are some numbers of magazine subscriptions Andre could sell and still reach his goal?
5. Write an inequality to represent that Andre wants to earn at least $68.
6. Write an inequality to represent the number of subscriptions Andre must sell to reach his goal.
Diego has budgeted $35 to buy shorts and socks for soccer. He needs 5 pairs of identical socks and a pair of shorts. The shorts he wants cost $19.95.
1. Write an expression for the total cost of the socks and shorts. Use to represent the price of one pair of socks.
2. Write and solve an equation that represents Diego spending exactly $35 on the socks and shorts.
3. List some other possible prices for the socks that would still allow Diego to stay within his budget.
4. Write an inequality to represent the amount Diego can spend on a single pair of socks.

Are You Ready for More?

14.3

Activity

Granola Bars and Savings

Kiran has $100. He wants to know how much he could spend each month to still have at least $25 left one year from now.
1. To represent this situation, Kiran writes the inequality . What does represent? Why is it negative?
2. Find some values of that would work for Kiran.
3. To express all the values that would work, should we use $'_' allowed only in math modex \leq \text{__}$ or $'_' allowed only in math modex \geq \text{__}$ ? Explain your reasoning.
A teacher wants to buy 9 boxes of granola bars for a school trip. Each box usually costs $7, but many grocery stores are having a sale on granola bars this week. Different stores are selling boxes of granola bars at different discounts.
1. If represents the dollar amount of the discount, then the amount the teacher will pay can be expressed as . What does the quantity represent?
2. The teacher has $36 to spend on the granola bars. The equation represents her spending all $36. Solve this equation. What does the solution mean in this situation?
3. The teacher does not have to spend all $36. Write an inequality that represents her spending at most $36.
4. The solution to this inequality must either look like $'_' allowed only in math modex \leq \text{__}$ or $'_' allowed only in math modex \geq \text{__}$ . Which one is it? Explain your reasoning.

Are You Ready for More?

Student Lesson Summary

We can write and solve inequalities to solve problems.

Example: Elena has $5 and sells pens for $1.50 each. Her goal is to save $20. We could solve the equation to find the number of pens, , that Elena needs to sell in order to save exactly $20. Adding to both sides of the equation gives us , and then dividing both sides by 1.5 gives the solution pens.

What if Elena wants to save more than $20? The inequality tells us that the amount of money Elena saves needs to be greater than $20. The solution to the previous equation will help us understand what the solutions to the inequality will be. We know that if Elena sells 10 pens, she will save exactly $20. Since each pen gives her more money, she needs to sell more than 10 pens to save more than $20. So, we can represent all the solutions to the inequality with another inequality: . A solution to an inequality is a number that can be used in place of the variable to make the inequality true.

Glossary

solution to an inequality

A solution to an inequality is a number that can be used in place of the variable to make the inequality true.

A solution to the inequality is 5, because it is true that .
Some other solutions to this inequality are 9.9, 0, and -4.