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

Question

?(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 \(-12g + 18 > -5g + 53\), let's first isolate \(g\).

1. Start by moving all terms involving \(g\) to one side and constant terms to the other side: \[ -12g + 5g > 53 - 18 \]

2. Combine like terms: \[ -7g > 35 \]

3. Now, divide both sides by -7. Remember that when you divide by a negative number, you have to reverse the inequality sign: \[ g < -5 \]

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

Therefore, the correct answer is:

g < −5 (g less than negative 5)