Find the root of the equation x - x/5 = -4/5.

Step-by-step solution

1. 1

   Notice that both left-hand terms are multiples of the same unknown. There is nothing to expand and no brackets to clear — this is a one-step equation once $x$ and $x/5$ are merged. Write the first term with the same denominator:

   $x=\frac{5x}{5}.$

2. 2

   Combine the like terms.

   $\frac{5x}{5}-\frac{x}{5}=\frac{5x-x}{5}=\frac{4x}{5},$

   so the equation collapses to

   $\frac{4x}{5}=-\frac{4}{5}.$

3. 3

   Clear the common denominator. Multiply both sides by $5$. Since the same factor of $5$ sits under both sides, it disappears cleanly:

   $4x=-4.$

4. 4

   Divide by the coefficient of x.

   $x=\frac{-4}{4}=-1.$

5. 5

   Substitute back into the original equation. With $x=-1$ the left side is

   $-1-\frac{-1}{5}=-1+\frac{1}{5}=-\frac{5}{5}+\frac{1}{5}=-\frac{4}{5},$

   which equals the right side, so $x=-1$ is the root.