Question

determine the solution set of 2x > -8 and -5x + 7 = 12
A. {x|x > -1}
B. {-4}
C. {-1}
D. {x|x > -4}

Answer 1

Let's solve each inequality and equation step by step.

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

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

2. Now, let's solve the equation \(-5x + 7 = 12\):

Subtract 7 from both sides:
\[
-5x = 12 - 7
\]
\[
-5x = 5
\]

Divide both sides by -5, remembering to flip the inequality sign:
\[
x = -1
\]

Now, we have two results:
- From \(2x > -8\), we have \(x > -4\) (let's call this Result 1).
- From \(-5x + 7 = 12\), we have \(x = -1\) (this is a specific solution, which we can call Result 2).

Next, let's check the given options:
- **A. {x|x > -1}**: This represents all numbers greater than -1.
- **B. {-4}**: This represents the specific number -4.
- **C. {-1}**: This represents the specific number -1.
- **D. {x|x > -4}**: This represents all numbers greater than -4.

Since we have:
- \(x > -4\) from the inequality, this matches with option **D. {x|x > -4}**.
- \(x = -1\) from the equation specifically gives us option **C. {-1}**, but it does not match the inequality solution.

Thus, the solution set that satisfies the inequality is:

**D. {x|x > -4}**.