Question

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

Answer 1

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

1. **Distribute both sides:**
\[
5(2k) - 5(3) \geq -3(4) + 3(3k)
\]
This simplifies to:
\[
10k - 15 \geq -12 + 9k
\]

2. **Rearrange the inequality:**
First, let's get all the terms involving \( k \) on one side and constant terms on the other side. We subtract \( 9k \) from both sides:
\[
10k - 9k - 15 \geq -12
\]
Simplifying that gives:
\[
k - 15 \geq -12
\]

3. **Isolate \( k \):**
Now, add 15 to both sides:
\[
k \geq -12 + 15
\]
This simplifies to:
\[
k \geq 3
\]

Thus, the solution to the inequality \( 5(2k - 3) \geq -3(4 - 3k) \) is:
\[
\boxed{k \geq 3}
\]