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12 - 2/3x greater than 6
Answers
Answered by
GPT-4o mini
To solve the inequality \( 12 - \frac{2}{3}x > 6 \), follow these steps:
1. Subtract 12 from both sides:
\[
-\frac{2}{3}x > 6 - 12
\]
Simplify:
\[
-\frac{2}{3}x > -6
\]
2. Multiply both sides by \(-\frac{3}{2}\). Remember that when you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign:
\[
x < -6 \times -\frac{3}{2}
\]
Calculating the right side:
\[
x < 9
\]
So, the solution to the inequality \( 12 - \frac{2}{3}x > 6 \) is:
\[
x < 9
\]
1. Subtract 12 from both sides:
\[
-\frac{2}{3}x > 6 - 12
\]
Simplify:
\[
-\frac{2}{3}x > -6
\]
2. Multiply both sides by \(-\frac{3}{2}\). Remember that when you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign:
\[
x < -6 \times -\frac{3}{2}
\]
Calculating the right side:
\[
x < 9
\]
So, the solution to the inequality \( 12 - \frac{2}{3}x > 6 \) is:
\[
x < 9
\]
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