Question

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

Answer 1

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

1. **Combine like terms**:
First, we can add \( 12g \) to both sides to move \( g \) terms to one side:
\[
18 > 7g + 53
\]

2. **Isolate the \( g \) term**:
Next, subtract \( 53 \) from both sides:
\[
18 - 53 > 7g
\]
\[
-35 > 7g
\]

3. **Divide by 7**:
Now, divide both sides by \( 7 \) (remember that dividing by a positive number does not change the direction of the inequality):
\[
-\frac{35}{7} > g
\]
Which simplifies to:
\[
-5 > g
\]

This can also be written as:
\[
g < -5
\]

So, the solution to the inequality is:
**g < -5**.