Section B Section B Checkpoint

Problem 1

3x+7=5x+73x + 7 = 5x + 7

  1. How many solutions does the equation have? Explain how you know without solving.
  2. Change 1 number in the equation 2x+4=2x+62x + 4 = 2x + 6 so that it has infinitely many solutions.
Show Solution
Solution
  1. 1 solution. Sample reasoning: The coefficients of xx on each side of the equation are not equal.
  2. Sample responses:
    • 2x+4=2x+42x + 4 = 2x+4
    • 2x+6=2x+62x + 6 = 2x+6
Show Sample Response
Sample Response
  1. 1 solution. Sample reasoning: The coefficients of xx on each side of the equation are not equal.
  2. Sample responses:
    • 2x+4=2x+42x + 4 = 2x+4
    • 2x+6=2x+62x + 6 = 2x+6

Problem 2

Two friends go out for a run.

  • Friend A runs at a steady pace of 160 meters per minute so that their distance from the starting line is represented by 160t160t.
  • Friend B gets started later and begins running a little further along the route so that their distance from the starting line is represented by 180(t−3)+100180(t-3)+100.
  1. Solve the equation 160t=180(t−3)+100160t = 180(t-3)+100. Show your reasoning.

  2. What does the solution mean in this situation?

Show Solution
Solution
  1. t=22t = 22. Sample reasoning: 160t=180t−540+100160t=180t - 540 + 100 by distributive property. 160t=180t−440160t = 180t - 440 by combining like terms. -20t=-440\text{-}20t = \text{-}440 by subtracting 180t180t from each side. t=22t = 22 by dividing each side by -20.
  2. Sample response: 22 minutes after Friend A started running the friends are the same distance from the starting line.
Show Sample Response
Sample Response
  1. t=22t = 22. Sample reasoning: 160t=180t−540+100160t=180t - 540 + 100 by distributive property. 160t=180t−440160t = 180t - 440 by combining like terms. -20t=-440\text{-}20t = \text{-}440 by subtracting 180t180t from each side. t=22t = 22 by dividing each side by -20.
  2. Sample response: 22 minutes after Friend A started running the friends are the same distance from the starting line.