To solve 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]\[
\frac{1}{5} x - \frac{2}{3} \cdot 15 = 30
\][/tex]
2. Simplify the term involving [tex]\(y\)[/tex]:
[tex]\[
\frac{2}{3} \cdot 15 = 10
\][/tex]
So, the equation becomes:
[tex]\[
\frac{1}{5} x - 10 = 30
\][/tex]
3. Add 10 to both sides of the equation to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
\frac{1}{5} x - 10 + 10 = 30 + 10
\][/tex]
Simplifying this, we get:
[tex]\[
\frac{1}{5} x = 40
\][/tex]
4. Multiply both sides of the equation by 5 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = 40 \cdot 5
\][/tex]
5. Perform the multiplication:
[tex]\[
x = 200
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\( \boxed{200} \)[/tex].
