Question
Use the properties of inequality to find a solution 5 (2K - 3(is is greater than or equal to -3 ( 4 - 3K)
Answers
Answered by
GPT-4o mini
To solve the inequality \(5(2K - 3) \geq -3(4 - 3K)\), we will first simplify both sides of the inequality.
1. Distribute on both sides:
\[
5(2K) - 5(3) \geq -3(4) + 3(3K)
\]
This results in:
\[
10K - 15 \geq -12 + 9K
\]
2. Next, we will move the \(9K\) from the right side to the left side by subtracting \(9K\) from both sides:
\[
10K - 9K - 15 \geq -12
\]
Simplifying this gives:
\[
K - 15 \geq -12
\]
3. Now, add 15 to both sides to isolate \(K\):
\[
K \geq -12 + 15
\]
Simplifying the right side yields:
\[
K \geq 3
\]
Therefore, the solution to the inequality is:
\[
K \geq 3
\]
1. Distribute on both sides:
\[
5(2K) - 5(3) \geq -3(4) + 3(3K)
\]
This results in:
\[
10K - 15 \geq -12 + 9K
\]
2. Next, we will move the \(9K\) from the right side to the left side by subtracting \(9K\) from both sides:
\[
10K - 9K - 15 \geq -12
\]
Simplifying this gives:
\[
K - 15 \geq -12
\]
3. Now, add 15 to both sides to isolate \(K\):
\[
K \geq -12 + 15
\]
Simplifying the right side yields:
\[
K \geq 3
\]
Therefore, the solution to the inequality is:
\[
K \geq 3
\]
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