Section A Section A Checkpoint

Problem 1

Answer each question, and explain or show your reasoning.

  1. Is 38\frac38 a solution to y+12=78y+\frac12=\frac78?
  2. Is 15 a solution to 0.4x=200.4x=20?
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Solution
  1. Yes. Sample reasoning: Substituting 38\frac38 for yy gives a true equation,  38+12=78\frac38+\frac12=\frac78.
  2. No. Sample reasoning:  Substituting 15 for xx gives the equation (0.4)⋅15=20(0.4) \boldcdot 15= 20, which is false.
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Sample Response
  1. Yes. Sample reasoning: Substituting 38\frac38 for yy gives a true equation,  38+12=78\frac38+\frac12=\frac78.
  2. No. Sample reasoning:  Substituting 15 for xx gives the equation (0.4)⋅15=20(0.4) \boldcdot 15= 20, which is false.

Problem 2

Solve each equation, and explain or show your reasoning.

  1. a+123=468a + 123 = 468
  2. 2.5b=20.52.5b=20.5
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Solution
  1. a=345a=345. Sample reasoning: Subtract 123123 from each side.
  2. b=8.2b=8.2. Sample reasoning: Divide each side by 2.52.5.
Show Sample Response
Sample Response
  1. a=345a=345. Sample reasoning: Subtract 123123 from each side.
  2. b=8.2b=8.2. Sample reasoning: Divide each side by 2.52.5.