To solve for the value of [tex]\( x \)[/tex] in the equation [tex]\( \frac{1}{5}x - \frac{2}{3}y = 30 \)[/tex] when [tex]\( y = 15 \)[/tex], follow these steps:
1. Substitute [tex]\( y = 15 \)[/tex] into the equation:
[tex]\[
\frac{1}{5}x - \frac{2}{3}(15) = 30
\][/tex]
2. Simplify the term involving [tex]\( y \)[/tex]:
[tex]\[
\frac{2}{3} \times 15 = \frac{2 \times 15}{3} = \frac{30}{3} = 10
\][/tex]
So the equation becomes:
[tex]\[
\frac{1}{5}x - 10 = 30
\][/tex]
3. Isolate the term involving [tex]\( x \)[/tex] by adding 10 to both sides of the equation:
[tex]\[
\frac{1}{5}x - 10 + 10 = 30 + 10
\][/tex]
This simplifies to:
[tex]\[
\frac{1}{5}x = 40
\][/tex]
4. Solve for [tex]\( x \)[/tex] by multiplying both sides of the equation by 5:
[tex]\[
x = 40 \times 5
\][/tex]
Therefore:
[tex]\[
x = 200
\][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( \boxed{200} \)[/tex].
