Which option is the solution to the inequality −12g+18>−5g+53

Question

?(1 point)
Responses

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

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

g>−5
g greater than negative 5

g<−5

Answer 1

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

1. First, isolate the terms involving \(g\) on one side and constant terms on the other side:

   \(-12g + 5g > 53 - 18\)

2. Simplify both sides:

   \(-7g > 35\)

3. To solve for \(g\), divide both sides by \(-7\). Remember to reverse the inequality sign when dividing by a negative number:

   \(g < \frac{35}{-7}\)

4. Simplify:

   \(g < -5\)

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

Thus, the correct option is:

g < −5