Question

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

{−1}
left brace negative 1 right brace

{x|x>−4}
left brace x vertical bar x greater than negative 4 right brace

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

{−4}

Answer 1

To solve the inequalities and equation, let's proceed step by step:

1. **Solve the inequality \(2x > -8\)**:
\[
2x > -8
\]
Divide both sides by 2:
\[
x > -4
\]
So, the solution set for the 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 (note that the inequality sign changes direction when dividing by a negative number):
\[
x = -1
\]

Now we have two results:
- From the inequality, we have the set \(\{x | x > -4\}\).
- From the equation, we found the single solution \(x = -1\).

To find a combined solution set that satisfies both the inequality and the equation, we see that \(x = -1\) is within the range defined by the inequality \(x > -4\).

Thus, the answer to the question is:

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

From the given options, the correct one is:
**\(\{x | x > -4\}\)** (left brace x vertical bar x greater than negative 4 right brace).