To determine the value of [tex]\( x \)[/tex] in the equation [tex]\( 2x + 3y = 36 \)[/tex] when [tex]\( y = 6 \)[/tex], follow these detailed steps:
1. Substitute [tex]\( y = 6 \)[/tex] into the equation:
The original equation is:
[tex]\[
2x + 3y = 36
\][/tex]
Replacing [tex]\( y \)[/tex] with 6, we get:
[tex]\[
2x + 3(6) = 36
\][/tex]
2. Simplify the equation:
Solve the part inside the parentheses first:
[tex]\[
3(6) = 18
\][/tex]
Now the equation becomes:
[tex]\[
2x + 18 = 36
\][/tex]
3. Isolate the term containing [tex]\( x \)[/tex] by subtracting 18 from both sides:
[tex]\[
2x + 18 - 18 = 36 - 18
\][/tex]
Simplifying both sides, we get:
[tex]\[
2x = 18
\][/tex]
4. Solve for [tex]\( x \)[/tex] by dividing both sides by 2:
[tex]\[
x = \frac{18}{2}
\][/tex]
Simplifying the division, we find:
[tex]\[
x = 9
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 6 \)[/tex] is [tex]\( \boxed{9} \)[/tex].
