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

Question

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
g less than negative 5

Answer 1

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

1. Start with the original inequality: \[ -12g + 18 > -5g + 53 \]

2. Add \(12g\) to both sides: \[ 18 > 7g + 53 \]

3. Subtract \(53\) from both sides: \[ 18 - 53 > 7g \] \[ -35 > 7g \]

4. Divide both sides by \(7\): \[ -5 > g \] or \[ g < -5 \]

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

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