Question

Which of these equations have no solution? Check all that apply. 2(x + 2) + 2 = 2(x + 3) + 1 2x + 3(x + 5) = 5(x – 3) 4(x + 3) = x + 12 4 – (2x + 5) = (–4x – 2) 5(x + 4) – x = 4(x + 5) – 1

Answer 1

Answer:

2(x + 2) + 2 = 2(x + 3) + 1

2x + 3(x + 5) = 5(x - 3)

5(x + 4) – x = 4(x + 5) – 1

Step-by-step explanation:

Answer 2

Answer:

• 2(x + 2) + 2 = 2(x + 3) + 1
• 2x + 3(x + 5) = 5(x – 3)
• 5(x + 4) – x = 4(x + 5) – 1

Step-by-step explanation:

It can be easier to see the answer if you subtract the right side of the equation from both sides, then simplify.

1. 2(x + 2) + 2 = 2(x + 3) + 1

  2(x + 2) + 2 - (2(x + 3) + 1) = 0

  2x +4 +2 -2x -6 -1 = 0

  -1 = 0 . . . . no solution

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2. 2x + 3(x + 5) = 5(x – 3)

  2x + 3(x + 5) - 5(x – 3) = 0

  2x +3x +15 -5x +15 = 0

  30 = 0 . . . . no solution

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3. 4(x + 3) = x + 12

  4(x + 3) - (x + 12) = 0

  4x +12 -x -12 = 0

  3x = 0 . . . . one solution, x=0

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4. 4 – (2x + 5) = (–4x – 2)

  4 – (2x + 5) - (–4x – 2) = 0

  4 -2x -5 +4x +2 = 0

  2x +1 = 0 . . . . one solution, x=-1/2

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5. 5(x + 4) – x = 4(x + 5) – 1

  5(x + 4) – x - (4(x + 5) – 1) = 0

  5x +20 -x -4x -20 +1 = 0

  1 = 0 . . . . no solution