Unit 3, Lesson 14
Finding Solutions to Inequalities in Context
Accelerated 7
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The table shows four inequalities and four values for . Decide whether each value makes each inequality true, and complete the table with “true” or “false”.
| 0 | 100 | -100 | 25 | |
|---|---|---|---|---|
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.
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.
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 and solve an equation that represents Diego spending exactly \$35 on the socks and shorts.
Write an inequality to represent the amount Diego can spend on a single pair of socks.
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.