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 proceed with the following steps:

1. Distribute both sides of the inequality:

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

2. Next, we want to isolate \( k \). First, we'll get all terms containing \( k \) on one side and constant terms on the other side. Subtract \( 9k \) from both sides:

   \[ 10k - 9k - 15 \geq -12 \] Which simplifies to: \[ k - 15 \geq -12 \]

3. Now, we will add 15 to both sides:

   \[ k \geq -12 + 15 \] This means: \[ k \geq 3 \]

Thus, the solution to the inequality is \( k \geq 3 \).

So, \( k \geq \textbf{3} \).

Answer 2

Rewrite the answer in an easier way to understand