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

Answer 1

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

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

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

   This simplifies to:

   \(-7g > 35\)

2. Divide both sides by -7: Remember that when you divide or multiply both sides of an inequality by a negative number, you must reverse the inequality sign.

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

   This simplifies to:

   \(g < -5\)

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

Therefore, the correct response is: g < -5.