Question

Solve the equation.
two sevenths plus one fifth x minus one fourth equals four fifths x
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Part 1
The solution is xequals
  
enter your response here.

Answer 1

To solve the equation:

\[
\frac{2}{7} + \frac{1}{5}x - \frac{1}{4} = \frac{4}{5}x
\]

First, let's isolate \(x\) on one side. Start by moving \(\frac{1}{5}x\) and \(\frac{1}{4}\) to the right side:

\[
\frac{2}{7} - \frac{1}{4} = \frac{4}{5}x - \frac{1}{5}x
\]

Subtract the fractions on the left side and combine the \(x\) terms on the right side:

\[
\frac{2}{7} - \frac{1}{4} = \left(\frac{4}{5} - \frac{1}{5}\right)x
\]

This simplifies to:

\[
\frac{2}{7} - \frac{1}{4} = \frac{3}{5}x
\]

Next, we need to combine \(\frac{2}{7}\) and \(-\frac{1}{4}\). To do this, we need to find a common denominator. The least common multiple of 7 and 4 is 28.

Convert both fractions:

\[
\frac{2}{7} = \frac{2 \times 4}{7 \times 4} = \frac{8}{28}
\]
\[
-\frac{1}{4} = -\frac{1 \times 7}{4 \times 7} = -\frac{7}{28}
\]

Now combine these:

\[
\frac{8}{28} - \frac{7}{28} = \frac{1}{28}
\]

So now our equation is:

\[
\frac{1}{28} = \frac{3}{5}x
\]

To isolate \(x\), multiply both sides by \(\frac{5}{3}\):

\[
x = \frac{1}{28} \times \frac{5}{3} = \frac{5}{84}
\]

Thus, the solution is:

\[
x = \frac{5}{84}
\]

Final answer:

**x equals \(\frac{5}{84}\)**.