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 will first simplify both sides.

Start by distributing on both sides: \[ 5(2k) - 5(3) \geq -3(4) + 3(3k) \] This simplifies to: \[ 10k - 15 \geq -12 + 9k \]

Next, we will get all terms involving \( k \) on one side and the constant terms on the other side. 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 gives: \[ k \geq 3 \]

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