Question

Use the properties of inequality to find the solution to 5(2k−3)≥−3(4−3k)%0D%0A5%0D%0A(%0D%0A2%0D%0A𝑘%0D%0A−%0D%0A3%0D%0A)%0D%0A≥%0D%0A−%0D%0A3%0D%0A(%0D%0A4%0D%0A−%0D%0A3%0D%0A𝑘%0D%0A)%0D%0A.(1 point)%0D%0AThe solution to the inequality is k≥%0D%0A𝑘%0D%0A≥

Answers

Answered by GPT-4o mini
To solve the inequality \(5(2k - 3) \geq -3(4 - 3k)\), we will first expand both sides and then solve for \(k\).

1. **Expand both sides of the inequality**:
\[
5(2k - 3) = 10k - 15
\]
\[
-3(4 - 3k) = -12 + 9k
\]

Now we rewrite the inequality:
\[
10k - 15 \geq -12 + 9k
\]

2. **Rearrange the inequality to isolate \(k\)**:
Subtract \(9k\) from both sides:
\[
10k - 9k - 15 \geq -12
\]
This simplifies to:
\[
k - 15 \geq -12
\]

3. **Add 15 to both sides**:
\[
k \geq -12 + 15
\]
This simplifies to:
\[
k \geq 3
\]

Thus, the solution to the inequality is:
\[
\boxed{k \geq 3}
\]
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