Use the properties of inequality to find the solution to 5(2k−3)≥−3(4−3k)

Question

.(1 point)
The solution to the inequality is k≥
.

Answer 1

To solve the inequality \( 5(2k - 3) \geq -3(4 - 3k) \), we will start by expanding both sides of the inequality.

1. Expand both sides:

   \[ 5(2k) - 5(3) \geq -3(4) + 3(3k) \] \[ 10k - 15 \geq -12 + 9k \]

2. 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