Question

Which option is the solution to the inequality −12g+18>−5g+53 ?(1 point) Responses g<−5 g less than negative 5 g>71−17 g greater than Start Fraction 71 over negative 17 End Fraction g<71−17 g less than Start Fraction 71 over negative 17 End Fraction g>−5 g greater than negative 5

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. This simplifies to:

\[ -7g > 35 \]

3. Now, divide both sides by \(-7\). Remember that when dividing or multiplying by a negative number, the direction of the inequality changes:

\[ g < -5 \]

Thus, the solution to the inequality is:

\[ g < -5 \]

So the correct option is: g < -5 (g less than negative 5).