Lesson 9
Dealing with Negative Numbers
Problem 1
Solve each equation.
- \(4x=\text-28\)
- \(x-\text-6=\text-2\)
- \(\text-x+4=\text-9\)
- \(\text-3x+7=1\)
- \(25x+\text-11=\text-86\)
Solution
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Problem 2
Here is an equation \(2x+9=\text-15\). Write three different equations that have the same solution as \(2x+9=\text-15\). Show or explain how you found them.
Solution
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Problem 3
Select all the equations that match the diagram.
![Tape diagram, 3 equal parts each marked x + 5, total 18.](https://staging-cms-im.s3.amazonaws.com/jPAWpQS54n1r8u91nRRnG8Rf?response-content-disposition=inline%3B%20filename%3D%227-7.6.A3.newPP.04.png%22%3B%20filename%2A%3DUTF-8%27%277-7.6.A3.newPP.04.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T080046Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=7c8a110956c718b027e6b289f90d6bd643702e7e8424a9b13c656e1a9143073a)
\(x+5=18\)
\(18\div3=x+5\)
\(3(x+5)=18\)
\(x+5 = \frac13\boldcdot 18\)
\(3x+5=18\)
Solution
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(From Unit 6, Lesson 3.)Problem 4
There are 88 seats in a theater. The seating in the theater is split into 4 identical sections. Each section has 14 red seats and some blue seats.
- Draw a tape diagram to represent the situation.
- What unknown amounts can be found by by using the diagram or reasoning about the situation?
Solution
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(From Unit 6, Lesson 2.)Problem 5
Match each story to an equation.
Solution
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(From Unit 6, Lesson 4.)