Which option is the solution to the inequality −12g+18>−5g+53

Question

?(1 point)
Responses

g<71−17
g less than Start Fraction 71 over negative 17 End Fraction

g>71−17
g greater than Start Fraction 71 over negative 17 End Fraction

g>−5
g greater than negative 5

g<−5

Answer 1

To solve the inequality \(-12g + 18 > -5g + 53\), we'll first isolate \(g\).

1. Start by adding \(12g\) to both sides:

\[ 18 > 7g + 53 \]

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

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

3. Now, divide both sides by \(7\):

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

This can be rewritten as:

\[ g < -5 \]

Thus, the solution to the inequality is:

g < -5