Question

Use the properties of inequality to find the solution to
$5(2k-3)\geqslant -3(4-3k)$ point)
The solution to the inequality is $k\geqslant $

Answer 1

To solve the inequality \( 5(2k-3) \geq -3(4-3k) \), we start by distributing on both sides.

First, distribute on the left-hand side:
\[
5(2k - 3) = 10k - 15
\]

Now distribute on the right-hand side:
\[
-3(4 - 3k) = -12 + 9k
\]

Now rewrite the inequality:
\[
10k - 15 \geq -12 + 9k
\]

Next, we want to isolate \( k \). Start by subtracting \( 9k \) from both sides:
\[
10k - 9k - 15 \geq -12
\]
This simplifies to:
\[
k - 15 \geq -12
\]

Next, add 15 to both sides:
\[
k \geq -12 + 15
\]
This simplifies further:
\[
k \geq 3
\]

Thus, the solution to the inequality is:
\[
\boxed{3}
\]