Question

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

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

{−1}
{
−
1
}
left brace negative 1 right brace

{−4}
{
−
4
}
left brace negative 4 right brace

{x|x>−4}

Answer 1

To solve the inequalities and equations you've provided, let's tackle them one by one.

1. **Inequality:** \(2x > -8\)

To solve for \(x\), divide both sides by 2:
\[
x > -4
\]
Thus, the solution set is:
\[
\{x|x > -4\}
\]

2. **Equation:** \(-5x + 7 = 12\)

First, isolate the term with \(x\):
\[
-5x = 12 - 7
\]
\[
-5x = 5
\]
Now, divide by -5:
\[
x = -1
\]
Thus, the solution set is:
\[
\{-1\}
\]

Now let's summarize the results:

- From the inequality \(2x > -8\), the solution set is \(\{x|x > -4\}\).
- From the equation \(-5x + 7 = 12\), the solution set is \(\{-1\}\).

Since the options available in your response do not specify mixing both results, here they are explicitly as derived:

- **Inequality solution:** \( \{x | x > -4\} \)
- **Equation solution:** \( \{-1\} \)

If you are asked to select just one based on the context, it will depend on which aspect of the problems is emphasized. However, both solutions are valid for their respective contexts. In the provided options, the closest match to the inequality solution is:
\(\{x | x > -4\}\).