To solve the inequality \( 5(2k - 3) \geq -3(4 - 3k) \), we will start by expanding both sides of the inequality.
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Expand both sides:
\[ 5(2k) - 5(3) \geq -3(4) + 3(3k) \] \[ 10k - 15 \geq -12 + 9k \]
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Now, rearrange the inequality to get all terms involving \( k \) on one side and constant terms on the other side:
\[ 10k - 9k \geq -12 + 15 \] \[ k \geq 3 \]
The solution to the inequality is \( k \geq 3 \). Therefore, the answer is:
k ≥ 3