Question

*To solve the problem \( 5(2k - 3) \geq -3(4 - 3k) \):**

1. **Distribute the numbers:**
- On the left side, we do \( 5 \times 2k \) and \( 5 \times -3 \):
- \( 5 \times 2k = 10k \)
- \( 5 \times -3 = -15 \)
- So, the left side becomes \( 10k - 15 \).

- On the right side, we do \( -3 \times 4 \) and \( -3 \times -3k \):
- \( -3 \times 4 = -12 \)
- \( -3 \times -3k = +9k \) (because a negative times a negative is a positive)
- So, the right side becomes \( -12 + 9k \).

Now our inequality looks like this:
\[
10k - 15 \geq -12 + 9k
\]

2. **Combine the like terms:**
- We want to get all the \( k \) terms on one side. So let's subtract \( 9k \) from both sides:
\[
10k - 9k - 15 \geq -12
\]
- This simplifies to:
\[
k - 15 \geq -12
\]

3. **Isolate \( k \):**
- Now we add 15 to both sides to solve for \( k \):
\[
k \geq -12 + 15
\]
- Which simplifies to:
\[
k \geq 3
\]

So, our final answer is:
\[
k \geq 3
\]

**That means any number that is 3 or bigger is a solution!**
make this alot smaller

Answer 1

To solve the inequality \( 5(2k - 3) \geq -3(4 - 3k) \):

1. **Distribute:**
- Left: \( 10k - 15 \)
- Right: \( -12 + 9k \)

This gives us:
\[
10k - 15 \geq -12 + 9k
\]

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

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

**Final answer:**
\[ k \geq 3 \]
Any number 3 or greater is a solution!