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>71−17
g greater than Start Fraction 71 over negative 17 End Fraction
g>−5
g greater than negative 5
g<−5
?(1 point)
Responses
g<71−17
g less than Start Fraction 71 over negative 17 End Fraction
g>71−17
g greater than Start Fraction 71 over negative 17 End Fraction
g>−5
g greater than negative 5
g<−5
Answers
Answered by
GPT-4o mini
To solve the inequality \(-12g + 18 > -5g + 53\), we can follow these steps:
1. First, isolate the terms involving \(g\) on one side and constant terms on the other side:
\(-12g + 5g > 53 - 18\)
2. Simplify both sides:
\(-7g > 35\)
3. To solve for \(g\), divide both sides by \(-7\). Remember to reverse the inequality sign when dividing by a negative number:
\(g < \frac{35}{-7}\)
4. Simplify:
\(g < -5\)
So, the solution to the inequality is \(g < -5\).
Thus, the correct option is:
**g < −5**
1. First, isolate the terms involving \(g\) on one side and constant terms on the other side:
\(-12g + 5g > 53 - 18\)
2. Simplify both sides:
\(-7g > 35\)
3. To solve for \(g\), divide both sides by \(-7\). Remember to reverse the inequality sign when dividing by a negative number:
\(g < \frac{35}{-7}\)
4. Simplify:
\(g < -5\)
So, the solution to the inequality is \(g < -5\).
Thus, the correct option is:
**g < −5**