3 answers
(click or scroll down)
Bot GPT 4-o mini To solve the inequalities and the equation given in the problem, we'll analyze each one step by step.
1. **Solving the inequality \(2x > -8\)**:
To isolate \(x\), divide both sides of the inequality by 2:
\[
x > -4
\]
2. **Solving the equation \(-5x + 7 = 12\)**:
First, subtract 7 from both sides:
\[
-5x = 12 - 7
\]
\[
-5x = 5
\]
Next, divide both sides by -5 (remember to reverse the inequality sign when dividing by a negative number):
\[
x = -1
\]
3. **Determining the solution set**:
The solution to the inequality \(x > -4\) gives us all numbers greater than -4, while the solution to the equation gives us a specific value \(x = -1\).
The solution set will depend on where these solutions overlap or what they suggest:
- The inequality \(x > -4\) indicates that any number greater than -4 is valid.
- The specific solution from the equation is \(x = -1\), which is valid since -1 is indeed greater than -4.
Given these analyses, we can select the correct representation of the solution sets:
- \( \{ x | x > -4 \} \) includes all numbers greater than -4, whereas \( \{ x | x > -1 \} \) would only include numbers greater than -1, which does not incorporate the entire range given by the inequality.
Thus, the solution set of the inequality and the equation is expressed as:
\[
\{ x | x > -4 \}
\]
So the correct answer is \(\{ x | x > -4 \}\).
37432