Question

Question

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

g>−5
g greater than negative 5

g<−5
g less 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. Rearrange the inequality: Move 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 or multiply both sides of an inequality by a negative number, you must reverse the inequality sign.

   \[g < \frac{35}{-7}\] \[g < -5\]

Thus, the solution to the inequality is:

\[g < -5\]

The correct option is:

g < −5 (g less than negative 5).