Answer :

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].