Certainly! Let's solve the given equation step by step:
The given equation is:
[tex]\[ 4(18 - 3k) = 9(k + 1) \][/tex]
1. Distribute on both sides:
[tex]\[
\text{Left side:} \quad 4 \cdot (18 - 3k)
\][/tex]
[tex]\[
4 \cdot 18 - 4 \cdot 3k = 72 - 12k
\][/tex]
[tex]\[
\text{Right side:} \quad 9 \cdot (k + 1)
\][/tex]
[tex]\[
9 \cdot k + 9 \cdot 1 = 9k + 9
\][/tex]
So now the equation becomes:
[tex]\[
72 - 12k = 9k + 9
\][/tex]
2. Combine like terms:
Move all terms involving [tex]\( k \)[/tex] to one side and constants to the other:
[tex]\[
72 - 9 = 9k + 12k
\][/tex]
[tex]\[
63 = 21k
\][/tex]
3. Solve for [tex]\( k \)[/tex]:
[tex]\[
21k = 63
\][/tex]
[tex]\[
k = \frac{63}{21}
\][/tex]
[tex]\[
k = 3
\][/tex]
Hence, the value of [tex]\( k \)[/tex] is:
[tex]\[ k = 3 \][/tex]
So, the solution to the equation [tex]\( 4(18 - 3k) = 9(k + 1) \)[/tex] is [tex]\( k = 3 \)[/tex].
