Question

Solve the equation.
StartFraction 5 left parenthesis x minus 1 right parenthesis Over 6 EndFraction minus x equals 1 minus StartFraction x Over 8 EndFraction

Answer 1

To solve the equation

\[
\frac{5(x - 1)}{6} - x = 1 - \frac{x}{8},
\]

we start by clearing the fractions. The least common multiple of the denominators 6 and 8 is 24. We can multiply the entire equation by 24 to eliminate the fractions:

\[
24 \left( \frac{5(x - 1)}{6} \right) - 24x = 24 \left( 1 - \frac{x}{8} \right).
\]

Simplifying each term gives:

\[
4 \cdot 5(x - 1) - 24x = 24 - 3x.
\]

This simplifies to:

\[
20(x - 1) - 24x = 24 - 3x.
\]

Expanding the left side:

\[
20x - 20 - 24x = 24 - 3x.
\]

Combining like terms on the left gives:

\[
-4x - 20 = 24 - 3x.
\]

Next, we'll get all terms involving \( x \) on one side and constants on the other. Adding \( 4x \) to both sides:

\[
-20 = 24 + x.
\]

Now, subtracting 24 from both sides gives:

\[
-20 - 24 = x,
\]

which simplifies to:

\[
-44 = x.
\]

Thus, the solution to the equation is

\[
\boxed{-44}.
\]