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
1 answer
To solve the inequality \( 5(2k - 3) \geq -3(4 - 3k) \), we follow these steps:
Distribute:
Now, rewriting the inequality: \[ 10k - 15 \geq -12 + 9k \]
Combine like terms: Subtract \( 9k \) from both sides: \[ 10k - 9k - 15 \geq -12 \] This simplifies to: \[ k - 15 \geq -12 \]
Isolate \( k \): Add 15 to both sides: \[ k \geq 3 \]
Thus, the solution is: \[ k \geq 3 \]
