Lesson 9
Dealing with Negative Numbers
Let’s show that doing the same to each side works for negative numbers too.
Problem 1
Solve each equation.
- \(4x=\text-28\)
- \(x-\text-6=\text-2\)
- \(\text-x+4=\text-9\)
- \(\text-3x+7=1\)
- \(25x+\text-11=\text-86\)
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.
Problem 3
Select all the equations that match the diagram.
![Tape diagram, 3 equal parts each marked x + 5, total 18.](https://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=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T162921Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=2dd127cfebc3f398524cead03e991d20a271f414492984a422c8d1f02899d7fe)
A:
\(x+5=18\)
B:
\(18\div3=x+5\)
C:
\(3(x+5)=18\)
D:
\(x+5 = \frac13\boldcdot 18\)
E:
(From Unit 6, Lesson 3.)
\(3x+5=18\)
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?
Problem 5
Match each story to an equation.