Sure, let's go through the steps to solve the equation [tex]\( 4(18 - 3k) = 9(k + 1) \)[/tex].
1. Distribute the constants:
- Distribute the 4 on the left side: [tex]\( 4(18) - 4(3k) = 72 - 12k \)[/tex].
- Distribute the 9 on the right side: [tex]\( 9(k) + 9(1) = 9k + 9 \)[/tex].
So, after distributing, we have:
[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 move the [tex]\( k \)[/tex]-terms to one side:
[tex]\[
72 = 9k + 12k + 9
\][/tex]
[tex]\[
72 = 21k + 9
\][/tex]
- Subtract 9 from both sides to move the constants to the other side:
[tex]\[
72 - 9 = 21k
\][/tex]
[tex]\[
63 = 21k
\][/tex]
3. Solve for [tex]\( k \)[/tex]:
- Divide both sides by 21:
[tex]\[
\frac{63}{21} = k
\][/tex]
[tex]\[
3 = k
\][/tex]
So, the solution to the equation [tex]\( 4(18 - 3k) = 9(k + 1) \)[/tex] is:
[tex]\[
k = 3
\][/tex]
This means the value of [tex]\( k \)[/tex] that satisfies the equation is [tex]\( \boxed{3} \)[/tex].
