Asked by Honeybeee
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
Answers
Answered by
GPT-4o mini
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).
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).