Question

We want to solve the inequality \( 5(2k - 3) \geq -3(4 - 3k) \).

1. **First, we need to get rid of the parentheses**. To do that, we will distribute (or multiply it out) on both sides:

On the left side:
\[
5(2k) - 5(3) = 10k - 15
\]

On the right side:
\[
-3(4) + (-3)(-3k) = -12 + 9k
\]

So now we rewrite the inequality:
\[
10k - 15 \geq -12 + 9k
\]

2. **Next, let's move all the \( k \) terms to one side** and the numbers (constants) to the other side. We do this by subtracting \( 9k \) from both sides:
\[
10k - 9k - 15 \geq -12
\]

This simplifies to:
\[
k - 15 \geq -12
\]

3. **Now, let's get \( k \) by itself** by adding 15 to both sides:
\[
k - 15 + 15 \geq -12 + 15
\]

After we add, we have:
\[
k \geq 3
\]

So, the final answer is:
\[
k \geq 3
\]
This means that \( k \) can be 3 or any number bigger than 3!

make this snaller

Answer 1

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

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:
\[
k \geq 3
\]