)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}

Answer 1

To determine the solution set for the inequalities and equations given, we need to solve each part separately.

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

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

Now we have the results:

• The solution set for \( 2x > -8 \) is \( { x | x > -4 } \).
• The solution for \( -5x + 7 = 12 \) is \( x = -1 \).

Since the question asks for the solution set involving both the inequality and the equation, we see that \( x = -1 \) falls within the solution set \( x > -4 \).

Therefore, the final combined solution will indicate the values of \( x \) satisfying the stated conditions.

Thus, the correct response for the solution set of the given problems is: \({ x | x > -4 }\) (this is the equivalent of the response option provided).