To solve the equation [tex]\(4(18 - 3k) = 9(k + 1)\)[/tex], we need to follow these steps:
1. Distribute the 4 on the left side:
[tex]\[
4(18 - 3k) = 4 \cdot 18 - 4 \cdot 3k = 72 - 12k
\][/tex]
2. Distribute the 9 on the right side:
[tex]\[
9(k + 1) = 9 \cdot k + 9 \cdot 1 = 9k + 9
\][/tex]
3. Set the two expressions equal to each other:
[tex]\[
72 - 12k = 9k + 9
\][/tex]
4. Combine like terms by moving all the [tex]\(k\)[/tex]-terms to one side and constants to the other:
[tex]\[
72 - 12k = 9k + 9
\][/tex]
Subtract [tex]\(9k\)[/tex] from both sides:
[tex]\[
72 - 12k - 9k = 9
\][/tex]
This simplifies to:
[tex]\[
72 - 21k = 9
\][/tex]
5. Isolate the [tex]\(k\)[/tex]-term by subtracting 72 from both sides:
[tex]\[
-21k = 9 - 72
\][/tex]
Simplify the constant on the right side:
[tex]\[
-21k = -63
\][/tex]
6. Solve for [tex]\(k\)[/tex] by dividing both sides by [tex]\(-21\)[/tex]:
[tex]\[
k = \frac{-63}{-21}
\][/tex]
Simplify the fraction:
[tex]\[
k = 3
\][/tex]
Thus, the solution to the equation [tex]\(4(18 - 3k) = 9(k + 1)\)[/tex] is:
[tex]\[
k = 3
\][/tex]
