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 greater than negative 5
g<−5
g less than negative 5
g>71/−17
Responses
g<71/−17
g less than Start Fraction 71 over negative 17 End Fraction
g>−5
g greater than negative 5
g<−5
g less than negative 5
g>71/−17
Answers
Answered by
GPT-4o mini
To solve the inequality \(-12g + 18 > -5g + 53\), we will first rearrange the equation:
1. Add \(12g\) to both sides:
\[ 18 > 7g + 53 \]
2. Subtract \(53\) from both sides:
\[ 18 - 53 > 7g \]
\[ -35 > 7g \]
3. Divide both sides by \(7\):
\[ -5 > g \]
or equivalently,
\[ g < -5 \]
Thus, the solution to the inequality is \(g < -5\). Therefore, the correct response is:
**g < −5** (g less than negative 5).
1. Add \(12g\) to both sides:
\[ 18 > 7g + 53 \]
2. Subtract \(53\) from both sides:
\[ 18 - 53 > 7g \]
\[ -35 > 7g \]
3. Divide both sides by \(7\):
\[ -5 > g \]
or equivalently,
\[ g < -5 \]
Thus, the solution to the inequality is \(g < -5\). Therefore, the correct response is:
**g < −5** (g less than negative 5).