IReady Lesson 26/Session 4

Lesson 26: 4 Using Substitution to Identify Solutions of Inequalities

By Chantele Quenard

Learning Targets:
•Use substitution to determine whether a given number in a specified set makes an inequality true.

•Write an inequality of the form x > c or
x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form
x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

Categorize

Options (3)

x > 0 could be used to represent the elevation of a mountain peak on land.

x    30 could be used to represent the number of days in a month.

x < –10 could be used to represent the number of days in a year.

Put the statement into the correct column.

Always

Sometimes

Never

Let's make sense of the problem..

Pilar has a gift card for a sporting goods store. She has $42.50 left on the card. She plans to buy one pair of yoga socks for $8. There are four other items that she is looking at.
What is the gist?

Let's make sense of the problem..

Pilar has a gift card for a sporting goods store. She has $42.50 left on the card. She plans to buy one pair of yoga socks for $8. There are four other items that she is looking at. Use the inequality x + 8  ≤   42.50, where x is the price of an item, to determine which of the other four items Pilar can buy. Discuss how to solve with your group.

Strategies:

You can use substitution to decide whether a value is a solution of an inequality. Substitute the price of each item for x in the inequality x + 8   ≤ 42.50.

Strategies:

You can use an equation and a graph to identify solutions of an inequality.

Think: For what value of x is x + 8 = 42.50?

          x + 8 = 42.50

    x + 8 – 8 = 42.50 – 8

                x = 34.50

If x is a value less than 34.50, x + 8 will be less than 42.50.

If x is a value greater than 34.50, x + 8 will be greater than 42.50.

Open Ended

Look at Model It. How do you know if a value is a solution of an inequality?

Multiple Select

Which numbers in the set {28.5, 30, 35.5, 38.5} are solutions of the inequality x + 8    42.50? Which of the items at the sporting goods store can Pilar buy?

• 28.5

• 30

• 35.5

• 38.5

Open Ended

How does solving the equation x + 8 = 42.50 help you identify solutions of the inequality x + 8 < 42.50?

Open Ended

Suppose you are given the inequality
10 > 2.5x along with a set of 20 values. Describe how you could decide which values are solutions of the inequality.

Open Ended

Aimee works up to 50 hours a month and earns $12 per hour. She wants to save more than $240 to buy a computer. The inequality 12h > 240, where h is the number of hours Aimee works this month, models this situation. Which values from 0 to 50 are solutions of the inequality? What do the solutions mean in this situation? Explain your reasoning.

Multiple Select

Which of the following values of c are solutions of the inequality c – 2 < 16? Select all that apply.

• 2

• 16

• 17.5

• 18

• 20

Draw

Hiroaki has 23 keychains in his collection.
He has a goal of collecting at least 30 keychains. He uses the inequality 30  ≤  23 + x, where x is a number of keychains, to represent how he can reach his goal. Which values in the set {6, 7, 8} are solutions of Hiroaki’s inequality?
Show your work.

Multiple Select

Hiroaki has 23 keychains in his collection.
He has a goal of collecting at least 30 keychains. He uses the inequality 30  ≤  23 + x, where x is a number of keychains, to represent how he can reach his goal.

Which values in the set {6, 7, 8} are solutions of Hiroaki’s inequality?

• 6

• 7

• 8