To solve the equation [tex]\( 4x + 2(x + 6) = 36 \)[/tex], follow the steps below:
1. Distribute the 2 to both terms inside the parentheses:
[tex]\[ 2(x + 6) \][/tex]
This distribution results in:
[tex]\[ 2x + 12 \][/tex]
2. Substitute this back into the equation:
[tex]\[ 4x + 2x + 12 = 36 \][/tex]
3. Combine like terms:
[tex]\[ 4x + 2x = 6x \][/tex]
Therefore, the equation becomes:
[tex]\[ 6x + 12 = 36 \][/tex]
4. Isolate the variable term (6x) by subtracting 12 from both sides of the equation:
[tex]\[ 6x + 12 - 12 = 36 - 12 \][/tex]
Simplifying this:
[tex]\[ 6x = 24 \][/tex]
5. Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 6:
[tex]\[ \frac{6x}{6} = \frac{24}{6} \][/tex]
Simplifying this:
[tex]\[ x = 4 \][/tex]
Thus, the solution to the equation [tex]\( 4x + 2(x + 6) = 36 \)[/tex] is:
[tex]\[ x = 4 \][/tex]
So the correct answer is:
[tex]\[
\boxed{x = 4}
\][/tex]
