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

Answer 1

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

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

2. **Divide both sides by \(-7\)**. Remember to reverse the inequality sign because we are dividing by a negative number:
\[
g < \frac{35}{-7}
\]
Simplifying gives:
\[
g < -5
\]

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

The correct option is:
- **g < -5**.