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 need to isolate \(g\).

1. Start by moving the terms involving \(g\) to one side and the constant terms to the other side. We can add \(12g\) to both sides:

   \[ 18 > 7g + 53 \]

2. Next, subtract \(53\) from both sides:

   \[ 18 - 53 > 7g \] \[ -35 > 7g \]

3. Now, divide both sides by \(7\) (remember to reverse the inequality sign when dividing by a negative number):

   \[ -5 > g \] or \[ g < -5 \]

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

So the correct response is:

g < −5 (g less than negative 5).