Use the properties of inequality to find the solution to 5(2k−3)≥−3(4−3k)%0D%0A5%0D%0A(%0D%0A2%0D%0A𝑘%0D%0A−%0D%0A3%0D%0A)%0D%0A≥%0D%0A−%0D%0A3%0D%0A(%0D%0A4%0D%0A−%0D%0A3%0D%0A𝑘%0D%0A)%0D%0A.(1 point)%0D%0AThe solution to the inequality is k≥%0D%0A𝑘%0D%0A≥

Answer 1

To solve the inequality \(5(2k - 3) \geq -3(4 - 3k)\), we will first expand both sides and then solve for \(k\).

1. Expand both sides of the inequality: \[ 5(2k - 3) = 10k - 15 \] \[ -3(4 - 3k) = -12 + 9k \]

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

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

3. Add 15 to both sides: \[ k \geq -12 + 15 \] This simplifies to: \[ k \geq 3 \]

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