Use the properties of inequality to find the solution to 5(2k−3)≥−3(4−3k) .(1 point)

Question

The solution to the inequality is k≥.

Answer 1

To solve the inequality \( 5(2k - 3) \geq -3(4 - 3k) \), we start by distributing both sides:

1. Distributing on the left side: \[ 5 \cdot 2k - 5 \cdot 3 = 10k - 15 \]

2. Distributing on the right side: \[ -3 \cdot 4 + 3 \cdot 3k = -12 + 9k \]

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

Next, we want to isolate \( k \). Let's subtract \( 9k \) from both sides: \[ 10k - 9k - 15 \geq -12 \] This simplifies to: \[ k - 15 \geq -12 \]

Now, add 15 to both sides: \[ k \geq -12 + 15 \] This simplifies to: \[ k \geq 3 \]

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