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:

\[
k \geq 3
\]