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

Question

1. **Distribute**:
- Left: \( 5(2k) - 5(3) = 10k - 15 \)
- Right: \( -3(4) + 9k = -12 + 9k \)

Now, rewriting the inequality:
\[
10k - 15 \geq -12 + 9k
\]

2. **Combine like terms**:
Subtract \( 9k \) from both sides:
\[
10k - 9k - 15 \geq -12
\]
This simplifies to:
\[
k - 15 \geq -12
\]

3. **Isolate \( k \)**:
Add 15 to both sides:
\[
k \geq 3
\]

Thus, the solution is:
\[
k \geq 3
\]make this smaller

Answer 1

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

1. Distribute:

   • Left: \( 5(2k) - 5(3) = 10k - 15 \)
   • Right: \( -3(4) + 9k = -12 + 9k \)

   Rewrite the inequality: \[ 10k - 15 \geq -12 + 9k \]

2. Combine like terms: Subtract \( 9k \) from both sides: \[ 10k - 9k - 15 \geq -12 \] Simplifying gives: \[ k - 15 \geq -12 \]

3. Isolate \( k \): Add 15 to both sides: \[ k \geq 3 \]

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