Question

Which option is the solution to the inequality −12g+18>−5g+53 ?(1 point)
Responses

g>71−17
g greater than Start Fraction 71 over negative 17 End Fraction

g>−5
g greater than negative 5

g<71−17
g less than Start Fraction 71 over negative 17 End Fraction

g<−5
g less than negative 5

Answer 1

To solve the inequality \(-12g + 18 > -5g + 53\), we can follow these steps:

1. Start with the original inequality:
\[
-12g + 18 > -5g + 53
\]

2. Add \(12g\) to both sides:
\[
18 > 7g + 53
\]

3. Subtract \(53\) from both sides:
\[
18 - 53 > 7g
\]
\[
-35 > 7g
\]

4. Divide both sides by \(7\):
\[
-5 > g
\]
or
\[
g < -5
\]

The solution to the inequality is \(g < -5\).

Thus, the correct response is:
**g < -5**.