Question

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

{x|x>−1}
start set x such that x is greater than negative 1 end set

{−4}
start set negative 4 end set

{x|x>−4}
start set x such that x is greater than negative 4 end set

{−1}

Answer 1

To find the solution set for the given inequalities and equations, we'll solve them one by one.

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

Divide both sides by 2:

\[
x > -4
\]

So the solution set for this inequality is:

\(\{x | x > -4\}\)

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

First, subtract 7 from both sides:

\[
-5x = 12 - 7
\]

\[
-5x = 5
\]

Now, divide both sides by -5 (remember to reverse the inequality because we're dividing by a negative):

\[
x = -1
\]

Now we can summarize the solutions:

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

Thus, the relevant solution sets are:

- \(\{x | x > -4\}\)
- \(\{-1\}\)

Since the question likely asks for a single solution set from the options given, the most relevant solution regarding \(x\) being greater than a certain value is:

**Answer**: \(\{x | x > -4\}\)