Lesson 3
Reasoning about Equations with Tape Diagrams
Problem 1
Solve each equation mentally.
- \(2x = 10\)
- \(\text-3x = 21\)
- \(\frac13 x = 6\)
- \(\text-\frac12x = \text-7\)
Solution
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(From Unit 5, Lesson 15.)Problem 2
Complete the magic squares so that the sum of each row, each column, and each diagonal in a grid are all equal.
![Three square grids.](https://cms-im.s3.amazonaws.com/5wKsRm7qGtcajwMSzoCPo7Xg?response-content-disposition=inline%3B%20filename%3D%227-7.5.PP.B.5.3.MagicSquare1.png%22%3B%20filename%2A%3DUTF-8%27%277-7.5.PP.B.5.3.MagicSquare1.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=20240630T171632Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=17f7d4241a2530dfe6d8f85c50982ef0437f7417379143652cb36214d4256ae8)
Solution
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(From Unit 5, Lesson 3.)Problem 3
Draw a tape diagram to match each equation.
-
\(5(x+1)=20\)
-
\(5x+1=20\)
Solution
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Problem 4
Select all the equations that match the tape diagram.
![Tape diagram, 1 part labeled 8, 6 parts labeled x, total 35.](https://cms-im.s3.amazonaws.com/4piXqQNBbX3fHUCGMkU9tvMo?response-content-disposition=inline%3B%20filename%3D%227-7.6.A3.newPP.01.png%22%3B%20filename%2A%3DUTF-8%27%277-7.6.A3.newPP.01.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=20240630T171632Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=ac1c41bfd9bc5072835f6c551354e1208d9045dc14723ad1457485b051bc5008)
\(35=8+x+x+x+x+x+x\)
\(35=8+6x\)
\(6+8x=35\)
\(6x+8=35\)
\(6x+8x=35x\)
\(35-8=6x\)
Solution
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Problem 5
Each car is traveling at a constant speed. Find the number of miles each car travels in 1 hour at the given rate.
-
135 miles in 3 hours
-
22 miles in \(\frac12\) hour
-
7.5 miles in \(\frac14\) hour
-
\(\frac{100}{3}\) miles in \(\frac23\) hour
-
\(97\frac12\) miles in \(\frac32\) hour
Solution
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(From Unit 4, Lesson 2.)