Question

Multiple Equations or Inequalities Quick Check
1 of 51 of 5 Items
Question
Determine the solution set of 2x>−8
and −5x+7=12
.(1 point)
Responses

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

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

{−4}
left brace negative 4 right brace

{−1}

Answer 1

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

1. **Solve the inequality:**

\( 2x > -8 \)

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 (remember that dividing by a negative swaps the inequality sign, but this is an equation):

\( x = -1 \)

Now, we can summarize the solutions:
- The solution for the inequality is \( \{x | x > -4\} \).
- The solution for the equation is \( \{-1\} \).

Therefore, the solution set that includes both the inequality and the equation results in:

The answer to choose is:
**{x | x > −4}**