Question

Which option is the solution to the inequality −12g+18>−5g+53−12g+18>−5g+53?(1 point)

Responses

g>71−17g>71−17

g greater than Start Fraction 71 over negative 17 End Fraction

g<71−17g<71−17

g less than Start Fraction 71 over negative 17 End Fraction

g>−5g>−5

g greater than negative 5

g<−5

Answer 1

To solve the inequality \(-12g + 18 > -5g + 53\), we can start by isolating \(g\).

1. Move \(-5g\) to the left side:
\[
-12g + 5g + 18 > 53
\]
Which simplifies to:
\[
-7g + 18 > 53
\]

2. Next, isolate the term with \(g\) by subtracting 18 from both sides:
\[
-7g > 53 - 18
\]
Which simplifies to:
\[
-7g > 35
\]

3. Now divide both sides by -7. Remember that dividing by a negative number reverses the inequality:
\[
g < \frac{35}{-7}
\]
Which simplifies to:
\[
g < -5
\]

The solution to the inequality is:
\[
g < -5
\]

So the correct option is:
**g < -5**.