Lesson 2
Keeping the Equation Balanced
Problem 1
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%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T235828Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=34abf3f2a82b83df10ed69c0b3c91abd642b272fc69f6dd02f77358d05cdccb5)
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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Problem 2
Here is a balanced hanger diagram.
Each triangle weighs 2.5 pounds, each circle weighs 3 pounds, and \(x\) represents the weight of each square. Select all equations that represent the hanger.
![A balanced hanger. Left side, 4 squares, 2 triangles, 2 circles. Right side, 2 squares, 1 triangle, 3 circles.](https://cms-im.s3.amazonaws.com/uqP5ncBED5WrQCNgFW2DgG5z?response-content-disposition=inline%3B%20filename%3D%228-8.4.B2.PP.hang7.png%22%3B%20filename%2A%3DUTF-8%27%278-8.4.B2.PP.hang7.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T235828Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=34ed1087ba77a51d6fc07d9832ae656f94058ee8e24740bcef44c3ba215f4b6b)
\(x+x+x+x+11=x+11.5\)
\(2x=0.5\)
\(4x+5+6=2x+2.5+6\)
\(2x+2.5=3\)
\(4x+2.5+2.5+3+3=2x+2.5+3+3+3\)
Solution
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Problem 3
What is the weight of a square if a triangle weighs 4 grams?
Explain your reasoning.
![Balanced hanger. Left side, 1 triangle, 2 squares. Right side, 3 triangles, 1 square.](https://cms-im.s3.amazonaws.com/5zwMaXudnndqJMHzdDAD5caD?response-content-disposition=inline%3B%20filename%3D%228-8.4.PP.B.Image.01.png%22%3B%20filename%2A%3DUTF-8%27%278-8.4.PP.B.Image.01.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T235828Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=ff2548e7d3946801ed0e4f52c469791ed6a3e3bb0598557ea80c9b1a1d82a5d3)
Solution
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Problem 4
Andre came up with the following puzzle. “I am three years younger than my brother, and I am 2 years older than my sister. My mom's age is one less than three times my brother's age. When you add all our ages, you get 87. What are our ages?”
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Try to solve the puzzle.
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Jada writes this equation for the sum of the ages: \((x)+(x+3)+(x-2) + 3(x+3) - 1=87\).
Explain the meaning of the variable and each term of the equation. -
Write the equation with fewer terms.
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Solve the puzzle if you haven’t already.
Solution
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(From Unit 4, Lesson 1.)Problem 5
These two lines are parallel. Write an equation for each.
![Two lines in an x y plane.](https://cms-im.s3.amazonaws.com/viuE8aXsi6oxvNPxJ1Zn5jJN?response-content-disposition=inline%3B%20filename%3D%228.3.B.PP.Image.09.png%22%3B%20filename%2A%3DUTF-8%27%278.3.B.PP.Image.09.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T235828Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=416bcc882fecea67313cc7a6ad6eca52866a09586ac116ed93b3737656f8473c)
Solution
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(From Unit 3, Lesson 8.)