Let's find the value of [tex]\( x \)[/tex] in the equation [tex]\(\frac{1}{5} x - \frac{2}{3} y = 30\)[/tex], given that [tex]\( y = 15 \)[/tex].
1. Start by substituting [tex]\( y = 15 \)[/tex] into the equation:
[tex]\[
\frac{1}{5} x - \frac{2}{3} \times 15 = 30
\][/tex]
2. Next, calculate [tex]\(\frac{2}{3} \times 15 \)[/tex]:
[tex]\[
\frac{2}{3} \times 15 = 10
\][/tex]
3. Substitute this value into the equation:
[tex]\[
\frac{1}{5} x - 10 = 30
\][/tex]
4. Add 10 to both sides of the equation to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
\frac{1}{5} x = 30 + 10
\][/tex]
5. Simplify the right side:
[tex]\[
\frac{1}{5} x = 40
\][/tex]
6. Finally, solve for [tex]\( x \)[/tex] by multiplying both sides by 5:
[tex]\[
x = 40 \times 5
\][/tex]
[tex]\[
x = 200
\][/tex]
Thus, the value of [tex]\( x \)[/tex] is 200.
