Section B Section B Checkpoint

Problem 1

Solve each equation. Explain or show your reasoning.

  1. 2(a+3.6)=442(a+3.6)=44
  2. 7p−8=−227p-8=-22
  3. -4(x+32)=16\text{-}4(x+\frac{3}{2})=16
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Solution
  1. a=18.4a=18.4. Sample reasoning: Students show dividing each side by 2 and subtracting 3.6 from each side.
  2. p=-2p=\text{-}2. Sample reasoning. Students show adding 8 to both sides and dividing both sides by 7.
  3. x=-112x=\text{-}\frac{11}{2}. Sample reasoning: Students show dividing each side by -4 and subtracting 32\frac32 from each side.
Show Sample Response
Sample Response
  1. a=18.4a=18.4. Sample reasoning: Students show dividing each side by 2 and subtracting 3.6 from each side.
  2. p=-2p=\text{-}2. Sample reasoning. Students show adding 8 to both sides and dividing both sides by 7.
  3. x=-112x=\text{-}\frac{11}{2}. Sample reasoning: Students show dividing each side by -4 and subtracting 32\frac32 from each side.

Problem 2

Andre ran 3.1 miles each day last week. This week he plans to increase the number of miles he runs each day so that he runs a total of 35 miles by the end of the week. He plans to run the same distance each day. What distance will Andre add to his run each day this week?
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Solution

1.9 miles. Sample responses:

  • $7(3.1+x)=35$ where $x$ is the increase in daily miles. $7(3.1+x)=35$, $3.1 + x = 5$, $x=1.9$
  • Students draw a tape diagram that shows 7 parts each labeled $3.1+x$ and a total of 35.
Show Sample Response
Sample Response

1.9 miles. Sample responses:

  • $7(3.1+x)=35$ where $x$ is the increase in daily miles. $7(3.1+x)=35$, $3.1 + x = 5$, $x=1.9$
  • Students draw a tape diagram that shows 7 parts each labeled $3.1+x$ and a total of 35.