Alright, let’s work through the solution step-by-step:
The problem at hand is to solve the equation [tex]\(4(18 - 3k) = 9(k + 1)\)[/tex].
1. Distribute the constants on both sides:
- Start by distributing the 4 on the left side:
[tex]\[
4(18 - 3k) = 4 \cdot 18 - 4 \cdot 3k = 72 - 12k
\][/tex]
- Next, distribute the 9 on the right side:
[tex]\[
9(k + 1) = 9k + 9
\][/tex]
2. Set the left side equal to the right side:
[tex]\[
72 - 12k = 9k + 9
\][/tex]
3. Combine like terms:
- To isolate the variable [tex]\(k\)[/tex], we move all [tex]\(k\)[/tex]-terms to one side and constants to the other:
[tex]\[
72 - 9 = 9k + 12k
\][/tex]
- Simplify the equation:
[tex]\[
63 = 21k
\][/tex]
4. Solve for [tex]\(k\)[/tex]:
- Divide both sides by 21 to get [tex]\(k\)[/tex]:
[tex]\[
k = \frac{63}{21}
\][/tex]
- Simplify the fraction:
[tex]\[
k = 3
\][/tex]
Therefore, the solution to the equation [tex]\(4(18 - 3k) = 9(k + 1)\)[/tex] is [tex]\(k = 3\)[/tex].
