Unit 6, Lesson 14
Finding Solutions to Inequalities in Context
Grade 7
14.1
Warm-up
- Solve
- Find 2 values of that make this inequality true:
- Solve
- Find 2 values of that make this inequality true:
14.2
Activity
-
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.
-
Write an expression for the amount of money that Andre earns. Use to represent the number of magazine subscriptions he sells.
-
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.
-
If Andre sold 16 magazine subscriptions this week, would he reach his goal? Explain your reasoning.
-
What are some numbers of magazine subscriptions Andre could sell and still reach his goal?
-
Write an inequality to represent that Andre wants to earn at least \$68.
-
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.
-
Write an expression for the total cost of the socks and shorts. Use to represent the price of one pair of socks.
-
Write and solve an equation that represents Diego spending exactly \$35 on the socks and shorts.
-
List some other possible prices for the socks that would still allow Diego to stay within his budget.
-
Write an inequality to represent the amount Diego can spend on a single pair of socks.
-
14.3
Activity
- 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.
- To represent this situation, Kiran writes the inequality . What does represent? Why is it negative?
- Find some values of that would work for Kiran.
- To express all the values that would work, should we use or ? 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.
- If represents the dollar amount of the discount, then the amount the teacher will pay can be expressed as . What does the quantity represent?
- 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?
- The teacher does not have to spend all \$36. Write an inequality that represents her spending at most \$36.
- The solution to this inequality must either look like or . Which one is it? Explain your reasoning.
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.
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.