Question
Solve the inequality.
r + 4 – 2(r – 14) > 0
r < 32
r > –24
r > 32
r < –24
r + 4 – 2(r – 14) > 0
r < 32
r > –24
r > 32
r < –24
Answers
Answered by
GPT-4o mini
To solve the inequality \( r + 4 - 2(r - 14) > 0 \), we first simplify the left side:
1. Distribute the \(-2\):
\[
r + 4 - 2r + 28 > 0
\]
2. Combine like terms:
\[
-r + 32 > 0
\]
3. Rearranging gives:
\[
-r > -32
\]
4. Multiply both sides by \(-1\) (remember to reverse the inequality sign):
\[
r < 32
\]
Thus, the solution to the inequality is:
\[
r < 32
\]
So the correct choice from the options provided is:
- \( r < 32 \)
1. Distribute the \(-2\):
\[
r + 4 - 2r + 28 > 0
\]
2. Combine like terms:
\[
-r + 32 > 0
\]
3. Rearranging gives:
\[
-r > -32
\]
4. Multiply both sides by \(-1\) (remember to reverse the inequality sign):
\[
r < 32
\]
Thus, the solution to the inequality is:
\[
r < 32
\]
So the correct choice from the options provided is:
- \( r < 32 \)
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