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Which of the following equations has a solution of −7

?(1 point)
Responses

−x+3=−4
negative x plus 3 equals negative 4

5x+11=−24
5 x plus 11 equals negative 24

4x−23=5
4 x minus 23 equals 5

−3x−8=−29

3 answers

To determine which equation has a solution of \( x = -7 \), we can substitute \(-7\) into each equation and see if it holds true.

  1. For \(-x + 3 = -4\): \[ -(-7) + 3 = -4 \implies 7 + 3 = -4 \implies 10 \neq -4 \] This equation does not have a solution of \(-7\).

  2. For \(5x + 11 = -24\): \[ 5(-7) + 11 = -24 \implies -35 + 11 = -24 \implies -24 = -24 \] This equation has a solution of \(-7\).

  3. For \(4x - 23 = 5\): \[ 4(-7) - 23 = 5 \implies -28 - 23 = 5 \implies -51 \neq 5 \] This equation does not have a solution of \(-7\).

  4. For \(-3x - 8 = -29\): \[ -3(-7) - 8 = -29 \implies 21 - 8 = -29 \implies 13 \neq -29 \] This equation does not have a solution of \(-7\).

The only equation that has a solution of \(-7\) is \(5x + 11 = -24\).

which one is the closes

To determine which equation is the closest to having a solution of \( x = -7 \), we can evaluate each equation by substituting \( x = -7 \) and seeing the resulting value. We will focus on how close each equation's resulting value is to the target outcome.

  1. For \(-x + 3 = -4\): \[ -(-7) + 3 = 7 + 3 = 10 \quad \text{(Difference: } 10 - (-4) = 14\text{)} \]

  2. For \(5x + 11 = -24\): \[ 5(-7) + 11 = -35 + 11 = -24 \quad \text{(Correct solution)} \]

  3. For \(4x - 23 = 5\): \[ 4(-7) - 23 = -28 - 23 = -51 \quad \text{(Difference: } -51 - 5 = -56\text{)} \]

  4. For \(-3x - 8 = -29\): \[ -3(-7) - 8 = 21 - 8 = 13 \quad \text{(Difference: } 13 - (-29) = 42\text{)} \]

Now, summarizing the differences:

  • From \(-x + 3 = -4\): Difference = 14
  • From \(5x + 11 = -24\): Difference = 0 (exact)
  • From \(4x - 23 = 5\): Difference = 56
  • From \(-3x - 8 = -29\): Difference = 42

Among these, the equation \(-x + 3 = -4\), with a difference of 14, is the closest incorrect equation to yielding the solution of \( x = -7\), while the correct equation is \(5x + 11 = -24\).