To find the value of [tex]\( x \)[/tex] in the equation [tex]\( 3x - 4y = 65 \)[/tex] when [tex]\( y = 4 \)[/tex], we can follow these steps:
1. Substitute the value of [tex]\( y \)[/tex] into the equation:
Given:
[tex]\[
3x - 4y = 65
\][/tex]
and [tex]\( y = 4 \)[/tex], we substitute 4 for [tex]\( y \)[/tex]:
[tex]\[
3x - 4(4) = 65
\][/tex]
2. Simplify the equation:
Calculate [tex]\( 4(4) \)[/tex]:
[tex]\[
4 \times 4 = 16
\][/tex]
Substitute 16 into the equation:
[tex]\[
3x - 16 = 65
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Add 16 to both sides of the equation to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
3x = 65 + 16
\][/tex]
This simplifies to:
[tex]\[
3x = 81
\][/tex]
Now, divide both sides by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{81}{3}
\][/tex]
This simplifies to:
[tex]\[
x = 27
\][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( 27 \)[/tex]. Therefore, the correct answer is:
[tex]\[
x = 27
\][/tex]
