Question

Which option is the solution to the inequality $-12g+18\gt -5g+53$ ? (1 point)
$g\gt \frac {71}{-17}$
$g\lt \frac {71}{-17}$
$g\lt -5$
$g\gt -5$

Answer 1

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

1. Start by getting all the terms involving \(g\) on one side. We can do this by adding \(12g\) to both sides:

\[
18 > 7g + 53
\]

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

\[
18 - 53 > 7g
\]

This simplifies to:

\[
-35 > 7g
\]

3. Now, we can divide both sides by \(7\). Remember to flip the inequality sign if we divide by a negative number, but since \(7\) is positive, we keep the inequality as is:

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

This simplifies to:

\[
-5 > g
\]

4. Interpreting this, we can rewrite it as:

\[
g < -5
\]

Thus, the solution to the inequality is

\[
g < -5
\]

So, among the options given, the correct answer is:

\[
\boxed{g < -5}
\]