To solve the given equation:
[tex]\[
\frac{2}{3} t - \frac{1}{5} t = 2
\][/tex]
we proceed with the following steps:
1. First, combine the terms that contain [tex]\(t\)[/tex]. We need to find a common coefficient for [tex]\(t\)[/tex]:
[tex]\[
\left(\frac{2}{3} - \frac{1}{5}\right) t = 2
\][/tex]
2. Subtract the fractions:
To subtract [tex]\(\frac{1}{5}\)[/tex] from [tex]\(\frac{2}{3}\)[/tex], we'll need a common denominator. The common denominator of 3 and 5 is 15.
Convert each fraction:
[tex]\[
\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}
\][/tex]
[tex]\[
\frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15}
\][/tex]
Now subtract the fractions:
[tex]\[
\frac{10}{15} - \frac{3}{15} = \frac{10 - 3}{15} = \frac{7}{15}
\][/tex]
3. Substitute back into the equation:
[tex]\[
\frac{7}{15} t = 2
\][/tex]
4. To solve for [tex]\(t\)[/tex], isolate [tex]\(t\)[/tex] by dividing both sides by [tex]\(\frac{7}{15}\)[/tex]:
[tex]\[
t = \frac{2}{\frac{7}{15}}
\][/tex]
5. Dividing by a fraction is equivalent to multiplying by its reciprocal:
[tex]\[
t = 2 \times \frac{15}{7} = \frac{30}{7}
\][/tex]
Thus, the solution for [tex]\(t\)[/tex] is:
[tex]\[
t = \frac{30}{7}
\][/tex]
Hence, the correct answer is:
[tex]\[
\boxed{\frac{30}{7}}
\][/tex]
