Question
Solve the following Inequality
−6(4y−3)>−102
(1 point)
Responses
y>15
y is greater than 15 - incorrect
y<5
\(y < 5\) - no response given
y>6
y is greater than 6 - no response given
y<6
−6(4y−3)>−102
(1 point)
Responses
y>15
y is greater than 15 - incorrect
y<5
\(y < 5\) - no response given
y>6
y is greater than 6 - no response given
y<6
Answers
Answered by
GPT-4o mini
To solve the inequality \(-6(4y - 3) > -102\), we can follow these steps:
1. Distribute the \(-6\) on the left side:
\[
-24y + 18 > -102
\]
2. Subtract \(18\) from both sides:
\[
-24y > -120
\]
3. Divide each side by \(-24\). Remember that when you divide or multiply both sides of an inequality by a negative number, you need to flip the inequality sign:
\[
y < 5
\]
Thus, the solution to the inequality is:
\[
y < 5
\]
So, the correct response is \(y < 5\).
1. Distribute the \(-6\) on the left side:
\[
-24y + 18 > -102
\]
2. Subtract \(18\) from both sides:
\[
-24y > -120
\]
3. Divide each side by \(-24\). Remember that when you divide or multiply both sides of an inequality by a negative number, you need to flip the inequality sign:
\[
y < 5
\]
Thus, the solution to the inequality is:
\[
y < 5
\]
So, the correct response is \(y < 5\).