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 {−4} left brace negative 4 right brace {−1} left brace negative 1 right brace {x|x>−4}

To determine the solution set for the two inequalities, we'll solve each one separately.

**1. Solve the inequality \(2x > -8\):**

Divide both sides by 2:

\[
x > -4
\]

So the solution set for this inequality is \( \{x | x > -4\} \).

**2. Solve the equation \(-5x + 7 = 12\):**

First, subtract 7 from both sides:

\[
-5x = 12 - 7
\]
\[
-5x = 5
\]

Now, divide both sides by -5 (remember to flip the inequality):

\[
x = -1
\]

So the solution for the equation is \(-1\).

**Summary of solution sets:**
- For \(2x > -8\), the solution set is \( \{x | x > -4\} \).
- For \(-5x + 7 = 12\), the solution set is \(-1\) (or \(\{-1\}\)).

If we consider the overall solutions, we can list them together as \( \{x | x > -4\} \) and \(\{-1\}\).

Thus, the responses given include \( \{x | x > -4\} \) and \(\{-1\}\). The correct solution set will depend on the context in which the question is being asked, typically shown as both of them. If you're choosing only one from the provided options, \( \{x | x > -4\} \) is likely the one you would choose, since it represents a broader range of solutions compared to a single point.

Select the response: **{x | x > −4}**.