Question

Use the properties of inequality to find a solution five times 2K - 3 is is greater than or equal to -3 * 4 - 3K

Answer 1

To solve the inequality \( 5(2K - 3) \geq -3 \cdot 4 - 3K \), we will first simplify both sides step by step.

1. Start by expanding the left side:
\[
5(2K - 3) = 10K - 15
\]

2. Now simplify the right side:
\[
-3 \cdot 4 = -12
\]
Thus,
\[
-3 \cdot 4 - 3K = -12 - 3K
\]

3. So now we can rewrite the inequality:
\[
10K - 15 \geq -12 - 3K
\]

4. Next, we will isolate \( K \). Start by adding \( 3K \) to both sides:
\[
10K + 3K - 15 \geq -12
\]
This simplifies to:
\[
13K - 15 \geq -12
\]

5. Next, add \( 15 \) to both sides:
\[
13K \geq -12 + 15
\]
Simplifying the right side gives:
\[
13K \geq 3
\]

6. Finally, divide both sides by \( 13 \):
\[
K \geq \frac{3}{13}
\]

Therefore, the solution to the inequality is:
\[
K \geq \frac{3}{13}
\]