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

Answer 1

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

1. Move the terms involving \(g\) to one side: \[ -12g + 5g > 53 - 18 \] This simplifies to: \[ -7g > 35 \]

2. Divide both sides by \(-7\). Remember to reverse the inequality sign because we are dividing by a negative number: \[ g < \frac{35}{-7} \] Simplifying gives: \[ g < -5 \]

So the solution to the inequality is: \[ g < -5 \]

The correct option is:

• g < -5.