Which option is the solution to the inequality −12g+18>−5g+53 ?(1 point) Responses g<−5 g less than negative 5 g>−5 g greater than negative 5 g>71−17 g greater than Start Fraction 71 over negative 17 End Fraction g<71−17

Answer 1

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

1. Combine like terms: Start by moving all terms involving \(g\) to one side and constant terms to the other side.

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

   This simplifies to: \(-7g > 35\)

2. Divide by -7: Remember that when you divide an inequality by a negative number, you need to reverse the inequality sign.

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

   Simplifying this gives: \(g < -5\)

Thus, the solution to the inequality is:

g < -5

So the correct response is g < −5.