Lesson 14
Finding Solutions to Inequalities in Context
Problem 1
The solution to \(53x > 35\) is either \(x>\text10\) or \(\text10>x\). Which solution is correct? Explain how you know.
Solution
For access, consult one of our IM Certified Partners.
Problem 2
The school band director determined from past experience that if they charge \(t\) dollars for a ticket to the concert, they can expect attendance of \(100050t\). 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?
Solution
For access, consult one of our IM Certified Partners.
Problem 3
Which inequality is true when the value of \(x\) is 3?
\(\textx 6 < \text3.5\)
\(\textx 6 >3.5\)
\(\textx 6 > \text3.5\)
\(x 6 > \text3.5\)
Solution
For access, consult one of our IM Certified Partners.
(From Unit 6, Lesson 13.)Problem 4
Draw the solution set for each of the following inequalities.

\(x\leq5\)

\(x<\frac52\)
Solution
For access, consult one of our IM Certified Partners.
(From Unit 6, Lesson 13.)Problem 5
Write three different equations that match the tape diagram.
Solution
For access, consult one of our IM Certified Partners.
(From Unit 6, Lesson 3.)Problem 6
A baker wants to reduce the amount of sugar in his cake recipes. He decides to reduce the amount used in 1 cake by \(\frac12\) cup. He then uses \(4\frac12\) cups of sugar to bake 6 cakes.
 Describe how the tape diagram represents the story.
 How much sugar was originally in each cake recipe?
Solution
For access, consult one of our IM Certified Partners.
(From Unit 6, Lesson 2.)Problem 7
One year ago, Clare was 4 feet 6 inches tall. Now Clare is 4 feet 10 inches tall. By what percentage did Clare’s height increase in the last year?
Solution
For access, consult one of our IM Certified Partners.
(From Unit 4, Lesson 12.)