Certainly! Let's solve the problem step by step.
### Problem:
Solve the equation [tex]\( 4(18 - 3k) = 9(k + 1) \)[/tex] for the variable [tex]\( k \)[/tex].
### Solution:
1. Distribute the constants on both sides:
Distributing [tex]\( 4 \)[/tex] on the left-hand side:
[tex]\[
4(18 - 3k) = 4 \cdot 18 - 4 \cdot 3k = 72 - 12k
\][/tex]
Distributing [tex]\( 9 \)[/tex] on the right-hand side:
[tex]\[
9(k + 1) = 9k + 9
\][/tex]
So, the equation now looks like:
[tex]\[
72 - 12k = 9k + 9
\][/tex]
2. Move all terms involving [tex]\( k \)[/tex] to one side and constants to the other side:
Add [tex]\( 12k \)[/tex] to both sides to gather all [tex]\( k \)[/tex]-terms on one side:
[tex]\[
72 = 21k + 9
\][/tex]
Subtract [tex]\( 9 \)[/tex] from both sides to gather all constants on the other side:
[tex]\[
63 = 21k
\][/tex]
3. Solve for [tex]\( k \)[/tex]:
Divide both sides by [tex]\( 21 \)[/tex] to isolate [tex]\( k \)[/tex]:
[tex]\[
k = \frac{63}{21} = 3
\][/tex]
So, the solution to the equation [tex]\( 4(18 - 3k) = 9(k + 1) \)[/tex] is:
[tex]\[
\boxed{3}
\][/tex]
