Lesson 14

Finding Solutions to Inequalities in Context

Let’s solve more complicated inequalities.

Problem 1

The solution to \(5-3x > 35\) is either \(x>\text-10\) or \(\text-10>x\). Which solution is correct? Explain how you know.

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 \(1000-50t\). 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?

Problem 3

Which inequality is true when the value of \(x\) is -3?


\(\text-x -6 < \text-3.5\)


\(\text-x- 6 >3.5\)


\(\text-x -6 > \text-3.5\)


\(x -6 > \text-3.5\)

(From Unit 6, Lesson 13.)

Problem 4

Draw the solution set for each of the following inequalities.

  1. \(x\leq5\)

    A number line with the numbers negative 10 through 9 indicated.
  2. \(x<\frac52\)

    A number line with the numbers negative 10 through 9 indicated.
(From Unit 6, Lesson 13.)

Problem 5

Write three different equations that match the tape diagram.

Tape diagram, 1 part labeled 19, 7 equal parts lableled x, total 40.


(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.

Tape diagram, 6 parts each labeled x minus 1 over 2, total 4 and 1 over 2.
  1. Describe how the tape diagram represents the story.
  2. How much sugar was originally in each cake recipe?
(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?

(From Unit 4, Lesson 12.)