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?
\(\text-x -6 < \text-3.5\)
\(\text-x- 6 >3.5\)
\(\text-x -6 > \text-3.5\)
\(x -6 > \text-3.5\)
Problem 4
Draw the solution set for each of the following inequalities.
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\(x\leq5\)
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\(x<\frac52\)
Problem 5
Write three different equations that match the tape diagram.
![Tape diagram, 1 part labeled 19, 7 equal parts lableled x, total 40.](https://cms-im.s3.amazonaws.com/WsAzRtYGxmssazWyUBR5EUZt?response-content-disposition=inline%3B%20filename%3D%227-7.6.A3.newPP.02.png%22%3B%20filename%2A%3DUTF-8%27%277-7.6.A3.newPP.02.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T162148Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=688e5d062c904dfe69d208b8fe57a1f5704e54160e37a89a2a55f625e9b038fa)
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.](https://cms-im.s3.amazonaws.com/mH8dBxJhdN3hzBiRpZP1M26S?response-content-disposition=inline%3B%20filename%3D%227.6.newPP.tapediagram.asdf.png%22%3B%20filename%2A%3DUTF-8%27%277.6.newPP.tapediagram.asdf.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T162148Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e5391df07c6582166d6bde5e047f276747da00dc094c2eb78198e3bd1c2242a3)
- Describe how the tape diagram represents the story.
- How much sugar was originally in each cake recipe?
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?