To determine 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], we will 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. Calculate [tex]\(\frac{2}{3} \cdot 15\)[/tex]:
[tex]\[
\frac{2}{3} \cdot 15 = \frac{2 \cdot 15}{3} = \frac{30}{3} = 10
\][/tex]
3. Substitute [tex]\(\frac{2}{3} \cdot 15\)[/tex] with 10 in the equation:
[tex]\[
\frac{1}{5} x - 10 = 30
\][/tex]
4. Add 10 to both sides of the equation to isolate [tex]\(\frac{1}{5} x\)[/tex]:
[tex]\[
\frac{1}{5} x - 10 + 10 = 30 + 10
\][/tex]
[tex]\[
\frac{1}{5} x = 40
\][/tex]
5. To solve for [tex]\( x \)[/tex], multiply both sides of the equation by 5:
[tex]\[
x = 40 \cdot 5
\][/tex]
[tex]\[
x = 200
\][/tex]
Thus, the value of [tex]\( x \)[/tex] is [tex]\( 200 \)[/tex].
