# Finding Solutions to Inequalities in Context

Warmup

Use the Pen tool to graph the inequality above the line before you check on the answer.

Activity #1

` Draw the Region Satisfying an Inequality on a Number Line. `

• Use the tools in the applet below to draw the solution set for each of the following inequalities.

(1.)

(2.)

(3.)

(4.)

(5.)

(6.)

Activity #2

` Application of Inequalities in Real Life.`

Andre has a summer job selling magazine subscriptions. He earns \$25 per week plus \$3 for every subscription he sells. Andre hopes to make at least enough money this week to buy a new pair of soccer cleats.

(1.) Let  represent the number of magazine subscriptions Andre sells this week. Write an expression for the amount of money he makes this week.

(2.) The least expensive pair of cleats Andre wants costs \$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 other numbers of magazine subscriptions Andre could have sold and still reached his goal?

(5.) Write an inequality expressing that Andre wants to make at least \$68.

(6.) Write an inequality to describe the number of subscriptions Andre must sell to reach his goal.

Activity #3

` Application of Inequalities to Solve Real World Problems.`

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 9(7 –). In this expression, what does the quantity 7 –represent?

(2.) The teacher has \$36 to spend on the granola bars. The equation 9(7 –) = 36 represents a situation where she spends all \$36. Solve this equation.

(3.) What does the solution mean in this situation?

(4.) The teacher does not have to spend all \$36. Write an inequality relating 36 and 9(7 –) representing this situation.

(5.) The solution to this inequality must either be   3 or  3. Which do you think is correct? Explain your reasoning.

Challenge #1

The school band director determined from past experience that if they charge dollars for a ticket to the concert, they can expect attendance of  The director used this model to figure out that the ticket price needs to be \$8 or greater in order for at least 600 to attend. Do you agree with this claim? Why or why not?

Challenge #2

The solution to 5 – 3> 35 is either > -10 or -10 >.

Challenge #3

Which inequality is true when the value of  is -3?

Quiz Time