Question

Question

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

Answer 1

To solve the inequality \( 5(2k - 3) \geq -3(4 - 3k) \), we can follow these steps:

1. Distribute both sides:

   \[ 5 \cdot 2k - 5 \cdot 3 \geq -3 \cdot 4 + 3 \cdot 3k \]

   This simplifies to:

   \[ 10k - 15 \geq -12 + 9k \]

2. Rearrange the inequality:

   To isolate \( k \), we can subtract \( 9k \) from both sides:

   \[ 10k - 9k - 15 \geq -12 \]

   This simplifies to:

   \[ k - 15 \geq -12 \]

3. Add 15 to both sides:

   \[ k \geq -12 + 15 \]

   Which simplifies to:

   \[ k \geq 3 \]

Thus, the solution to the inequality is:

\[ k \geq 3 \]