Question

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

{−1}
start set negative 1 end set

{−4}
start set negative 4 end set

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

{x|x>−4}

Answer 1

To solve the given inequalities and equation:

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

Divide both sides by 2:
\[
x > -4
\]
So, this gives us the solution set:
\[
\{x | x > -4\}
\]

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

Subtract 7 from both sides:
\[
-5x = 5
\]
Now divide by -5:
\[
x = -1
\]

Now we have two results:
- The inequality gives \(x > -4\).
- The equation gives the specific solution \(x = -1\).

Since \(-1\) is a number that is greater than \(-4\), it satisfies the condition from the inequality.

Now, considering the options provided:
1. \(\{-1\}\)
2. \(\{-4\}\)
3. \(\{x | x > -1\}\)
4. \(\{x | x > -4\}\)

The solution set based on the inequality \(x > -4\) is represented as:
\(\{x | x > -4\}\).

Though \(-1\) is a solution from the equation, the overall solution set that encompasses the inequality is broader.

Thus, the best answer from the options given is:
\(\{x | x > -4\}\).