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Indicate the number of solutions that each of these equations has by placing a checkmark in the appropriate column of the chart. A u + 2 = u + 5 No Solution One Solution Infinitely Many Solutions B w + 2 = 2w + 5 No Solution One Solution Infinitely Many Solutions C 3(w + 2) = 4(w + 2) No Solution One Solution Infinitely Many Solutions D 3(2x + 5) - x = 5(x + 3) No Solution One Solution Infinitely Many Solutions

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sqdancefan

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Answer:

  • No Solution: A
  • One Solution: B, C
  • Infinitely Many Solutions: D

Step-by-step explanation:

Simplified, you will find the equations to be in one of three forms:

  0 = 0 . . . . infinite solutions

  a = 0 . . . . a≠0, no solutions

  ax +b = 0 . . . one solution

To get one of these forms, we can subtract the right side of the equation from both sides, then simplify.

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A. (u +2) -(u +5) = 0

  -3 = 0 . . . . no solutions

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B. (w +2) -(2w +5) = 0

  -w -3 = 0 . . . . one solution

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C. 3(w+2) -4(w+2) = 0

  -w -2 = 0 . . . . one solution

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D. (3(2x +5) -x) -(5(x +3)) = 0

  6x +15 -x -5x -15 = 0

  0 = 0 . . . . infinitely many solutions

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