Question

Solve for xx. Express your answer as a proper or improper fraction in simplest terms.
minus, one eigth, equals, minus, one third, x, minus, start fraction, 7, divided by, 8, end fraction
−
8
1
​
=
−
3
1
​
x−
8
7
​

Answer 1

To solve the equation

\[
-\frac{1}{8} = -\frac{1}{3}x - \frac{7}{8},
\]

first, we'll eliminate the fraction on the right side by isolating \(-\frac{1}{3}x\). We can do this by adding \(\frac{7}{8}\) to both sides of the equation:

\[
-\frac{1}{8} + \frac{7}{8} = -\frac{1}{3}x.
\]

Calculating the left-hand side:

\[
-\frac{1}{8} + \frac{7}{8} = \frac{6}{8} = \frac{3}{4}.
\]

Now our equation looks like:

\[
\frac{3}{4} = -\frac{1}{3}x.
\]

Next, to solve for \(x\), we can multiply both sides by \(-3\) to eliminate the fraction:

\[
-3 \cdot \frac{3}{4} = x.
\]

Calculating the left-hand side gives:

\[
-\frac{9}{4} = x.
\]

Thus, we have

\[
x = -\frac{9}{4}.
\]

This is the solution. The answer, expressed as a proper or improper fraction in simplest terms, is:

\[
\boxed{-\frac{9}{4}}.
\]