Lesson 14
Strategic Solving
Problem 1
Solve each of these equations. Explain or show your reasoning.
\(2b+8-5b+3=\text-13+8b-5\)
\(2x+7-5x+8=3(5+6x)-12x\)
\(2c-3=2(6-c)+7c\)
Solution
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Problem 2
Solve each equation and check your solution.
\(\text-3w-4=w+3\)
\(3(3-3x)=2(x+3)-30\)
\(\frac13(z+4)-6=\frac23(5-z)\)
Solution
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Problem 3
Elena said the equation \(9x+15=3x+15\) has no solutions because \(9x\) is greater than \(3x\). Do you agree with Elena? Explain your reasoning.
Solution
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Problem 4
Which of the changes would keep the hanger in balance?
Select all that apply.
![Balanced hanger. Left side, 1 triangle and 1 square. Right side, 2 circles and 1 triangle.](https://cms-im.s3.amazonaws.com/KMV6qwQ1QzkD3u6FJPuG1uFs?response-content-disposition=inline%3B%20filename%3D%228-8.4.PP.B.Image.06.png%22%3B%20filename%2A%3DUTF-8%27%278-8.4.PP.B.Image.06.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=20240630T181948Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=4b3794c31e2111719261c02012b55721b09f498d145b1c21f6da18e7c82d73ca)
Adding two circles on the left and a square on the right
Adding 2 triangles to each side
Adding two circles on the right and a square on the left
Adding a circle on the left and a square on the right
Adding a triangle on the left and a square on the right
Solution
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(From Unit 4, Lesson 12.)