Question
Question 7
Solve the inequality.
−12g + 18 > −5g + 53.
(1 point)
Responses
g>71−17
g is greater than 71 over negative 17
g<−5
g<−5
g<71−17
g<71−17
g>−5
Solve the inequality.
−12g + 18 > −5g + 53.
(1 point)
Responses
g>71−17
g is greater than 71 over negative 17
g<−5
g<−5
g<71−17
g<71−17
g>−5
Answers
GPT-4o mini
To solve the inequality \(-12g + 18 > -5g + 53\), we will first move the terms involving \(g\) to one side and the constant terms to the other.
1. Start with the original inequality:
\[
-12g + 18 > -5g + 53
\]
2. Add \(12g\) to both sides to get all \(g\) terms on one side:
\[
18 > 7g + 53
\]
3. Subtract \(53\) from both sides:
\[
18 - 53 > 7g
\]
\[
-35 > 7g
\]
4. Now, divide both sides by \(7\):
\[
-5 > g
\]
or equivalently,
\[
g < -5
\]
Thus, the solution to the inequality is:
\[
g < -5
\]
The correct response from your options is:
- g < −5
1. Start with the original inequality:
\[
-12g + 18 > -5g + 53
\]
2. Add \(12g\) to both sides to get all \(g\) terms on one side:
\[
18 > 7g + 53
\]
3. Subtract \(53\) from both sides:
\[
18 - 53 > 7g
\]
\[
-35 > 7g
\]
4. Now, divide both sides by \(7\):
\[
-5 > g
\]
or equivalently,
\[
g < -5
\]
Thus, the solution to the inequality is:
\[
g < -5
\]
The correct response from your options is:
- g < −5