Question

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

g < -5
g < -5

g>71−17
g is greater than 71 over negative 17

g > -5

Answer 1

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

1. Move the terms involving \(g\) to one side and the constant terms to the other side:
\[
-12g + 5g > 53 - 18
\]
This simplifies to:
\[
-7g > 35
\]

2. Now, divide both sides by \(-7\). Remember that when dividing or multiplying both sides of an inequality by a negative number, the inequality sign flips:
\[
g < \frac{35}{-7}
\]
Which simplifies to:
\[
g < -5
\]

The solution to the inequality is:
\[
g < -5
\]

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