Question

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

(Remember, when solving linear inequalities, if you multiply or divide both sides by a negative number, the inequality symbol must flip.)

(1 point)
Responses

g<−5
g<−5

g<71−17
g<71−17

g>71−17
g is greater than 71 over negative 17

g>−5
g is greater than negative 5

Answer 1

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

1. Start by adding \(5g\) to both sides:

\[
-12g + 5g + 18 > 53
\]

This simplifies to:

\[
-7g + 18 > 53
\]

2. Next, subtract 18 from both sides:

\[
-7g > 53 - 18
\]

This gives us:

\[
-7g > 35
\]

3. Now, divide both sides by -7. Remember, when dividing by a negative number, we must flip the inequality symbol:

\[
g < \frac{35}{-7}
\]

This simplifies to:

\[
g < -5
\]

So, the solution to the inequality is:

**g < −5**.

The correct option is:

**g < -5**.