To find the value of [tex]\( x \)[/tex] in the given equation:
[tex]\[
\frac{4}{5} x - \frac{1}{10} = \frac{3}{10}
\][/tex]
we will proceed step-by-step to isolate [tex]\( x \)[/tex].
1. Eliminate the fraction by finding a common denominator, if necessary:
The denominators in the equation are 5 and 10. The common denominator between 5 and 10 is 10.
2. Rewrite the equation with the common denominator:
- [tex]\(\frac{4}{5} x\)[/tex] can be rewritten as [tex]\(\frac{8}{10} x\)[/tex] because [tex]\(\frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10}\)[/tex].
So, the equation becomes:
[tex]\[
\frac{8}{10} x - \frac{1}{10} = \frac{3}{10}
\][/tex]
3. Isolate the term with [tex]\( x \)[/tex]:
Add [tex]\(\frac{1}{10}\)[/tex] to both sides to get:
[tex]\[
\frac{8}{10} x = \frac{3}{10} + \frac{1}{10}
\][/tex]
4. Combine the fractions on the right-hand side:
[tex]\[
\frac{8}{10} x = \frac{4}{10}
\][/tex]
5. Divide both sides by [tex]\(\frac{8}{10}\)[/tex] to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{\frac{4}{10}}{\frac{8}{10}} = \frac{4}{10} \times \frac{10}{8} = \frac{4}{8} = \frac{1}{2}
\][/tex]
Thus, [tex]\( x = \frac{1}{2} \)[/tex].
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( \frac{1}{2} \)[/tex]. Hence, the correct answer is:
[tex]\[
\boxed{\frac{1}{2}}
\][/tex]
