Question

Determine the solution set of 2x>−8 and −5x+7=12 .(1 point) Responses {x|x>−4} left brace x vertical bar x greater than negative 4 right brace {−4} left brace negative 4 right brace {−1} left brace negative 1 right brace {x|x>−1}

Answer 1

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

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

Divide both sides by 2:
\[
x > -4
\]

This means that the solution set is \( \{ x \mid x > -4 \} \).

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

First, we subtract 7 from both sides:
\[
-5x = 12 - 7
\]
\[
-5x = 5
\]

Next, divide both sides by -5:
\[
x = -1
\]

This gives us the solution \( \{-1\} \).

Now we combine the solution sets:

- From the inequality \(2x > -8\), we have \( \{ x \mid x > -4 \} \).
- From the equation \(-5x + 7 = 12\), we have \( \{-1\} \).

Both solutions are valid in their own contexts. However, since \(-1\) does not contradict the inequality \(x > -4\), we can consider both parts together.

Thus, the overall range of solutions can be expressed as combining \( \{ x \mid x > -4 \} \) and the specific point \( \{-1\} \).

The best representation from the provided response options for the solution of the inequality \(x > -4\) is:

\[
\{ x \mid x > -4 \}
\]

Thus, the final answer is:

**{x | x > -4} (left brace x vertical bar x greater than negative 4 right brace)**