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Determine the solution set of 2x>−8 and −5x+7=12 .(1 point)

Responses

{x|x>−1}
left brace x vertical bar x greater than negative 1 right brace

{x|x>−4}
left brace x vertical bar x greater than negative 4 right brace

{−4}
left brace negative 4 right brace

{−1}

1 answer

Let's solve the two inequalities and equations step-by-step.

  1. Solve the inequality \(2x > -8\): \[ x > \frac{-8}{2} \] \[ x > -4 \]

  2. Solve the equation \(-5x + 7 = 12\): \[ -5x = 12 - 7 \] \[ -5x = 5 \] \[ x = \frac{5}{-5} \] \[ x = -1 \]

Now we have two statements:

  • From the inequality \(2x > -8\), we found \(x > -4\).
  • From the equation \(-5x + 7 = 12\), we found \(x = -1\).

The solution set that satisfies both statements is:

  1. \(x = -1\) is included in the solution of \(x > -4\) (since \(-1 > -4\)).

Thus, the solution set for this problem is \({-1}\).

Therefore, the correct response is: {−1}