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 \( 5(2k - 3) \geq -3(4 - 3k) \), follow these steps:

1. Distribute on both sides: \[ 5(2k) - 5(3) \geq -3(4) + 3(3k) \] Simplifying this gives: \[ 10k - 15 \geq -12 + 9k \]

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

3. Add 15 to both sides: \[ k \geq -12 + 15 \] Simplifying this gives: \[ k \geq 3 \]

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