Question
Question 7
Solve the inequality.
−12g + 18 > −5g + 53.
(1 point)
Responses
g<71−17
g<71−17
g>−5
g is greater than negative 5
g>71−17
g is greater than 71 over negative 17
g<−5
Solve the inequality.
−12g + 18 > −5g + 53.
(1 point)
Responses
g<71−17
g<71−17
g>−5
g is greater than negative 5
g>71−17
g is greater than 71 over negative 17
g<−5
Answers
GPT-4o mini
To solve the inequality \(-12g + 18 > -5g + 53\), we can follow these steps:
1. First, let's isolate the terms involving \(g\) on one side and the constant terms on the other side. Start by adding \(12g\) to both sides:
\[-12g + 12g + 18 > -5g + 12g + 53\]
This simplifies to:
\[18 > 7g + 53\]
2. Next, subtract \(53\) from both sides:
\[18 - 53 > 7g\]
Simplifying the left side gives:
\[-35 > 7g\]
3. Now, divide both sides by \(7\) (and remember to reverse the inequality since dividing by a negative value reverses the inequality):
\[\frac{-35}{7} > g\]
This simplifies to:
\[-5 > g\]
4. We can rewrite this in a more standard form:
\[g < -5\]
Thus, the solution to the inequality is:
**g < -5**
1. First, let's isolate the terms involving \(g\) on one side and the constant terms on the other side. Start by adding \(12g\) to both sides:
\[-12g + 12g + 18 > -5g + 12g + 53\]
This simplifies to:
\[18 > 7g + 53\]
2. Next, subtract \(53\) from both sides:
\[18 - 53 > 7g\]
Simplifying the left side gives:
\[-35 > 7g\]
3. Now, divide both sides by \(7\) (and remember to reverse the inequality since dividing by a negative value reverses the inequality):
\[\frac{-35}{7} > g\]
This simplifies to:
\[-5 > g\]
4. We can rewrite this in a more standard form:
\[g < -5\]
Thus, the solution to the inequality is:
**g < -5**