To solve the equation [tex]\( 3x - 4y = 65 \)[/tex] for [tex]\( x \)[/tex] when [tex]\( y = 4 \)[/tex], follow these steps:
1. Substitute [tex]\( y = 4 \)[/tex] into the equation:
[tex]\[
3x - 4(4) = 65
\][/tex]
2. Simplify the equation:
[tex]\[
3x - 16 = 65
\][/tex]
3. Add 16 to both sides to isolate [tex]\( 3x \)[/tex]:
[tex]\[
3x - 16 + 16 = 65 + 16
\][/tex]
[tex]\[
3x = 81
\][/tex]
4. Divide both sides of the equation by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[
\frac{3x}{3} = \frac{81}{3}
\][/tex]
[tex]\[
x = 27
\][/tex]
Thus, the value of [tex]\( x \)[/tex] when [tex]\( y = 4 \)[/tex] is [tex]\( x = 27 \)[/tex].
So, the correct answer is [tex]\( \boxed{x = 27} \)[/tex].
