Question

4/5x-5-=1/4
solve the solution below
4/5x=
x=

Answer 1

To solve the equation \( \frac{4}{5}x - 5 = \frac{1}{4} \), we first isolate the term with \( x \).

1. **Add 5 to both sides:**

\[
\frac{4}{5}x - 5 + 5 = \frac{1}{4} + 5
\]

This simplifies to:

\[
\frac{4}{5}x = \frac{1}{4} + 5
\]

To combine \( \frac{1}{4} \) and \( 5 \), we can express \( 5 \) as a fraction:

\[
5 = \frac{20}{4}
\]

Thus,

\[
\frac{4}{5}x = \frac{1}{4} + \frac{20}{4} = \frac{21}{4}
\]

2. **Now we have:**

\[
\frac{4}{5}x = \frac{21}{4}
\]

3. **Multiply both sides by the reciprocal of \( \frac{4}{5} \), which is \( \frac{5}{4} \):**

\[
x = \frac{21}{4} \cdot \frac{5}{4} = \frac{21 \cdot 5}{4 \cdot 4} = \frac{105}{16}
\]

Thus, the solution for \( x \) is:

\[
x = \frac{105}{16}
\]

To summarize:

\[
\frac{4}{5}x = \frac{21}{4}, \quad x = \frac{105}{16}
\]