Question

Solve (2/3)-(1/x)=5/6

Answer 1

$\frac{2}{3} - \frac{1}{x} = \frac{5}{6}$   Multiply both sides by 3
$2 - \frac{1(3)}{x} = \frac{5(3)}{6}$   Simplify the numerators
$2 - \frac{3}{x} = \frac{15}{6}$   Multiply both sides by 6
$12 - \frac{3(6)}{x} = 15$   Simplify the numerator
$12 - \frac{18}{x} = 15$   Multiply both sides by x
12x - 18 = 15x   Subtract 12x from both sides
       -18 = 3x    Divide both sides by 3
        -6 = x      Switch the sides to make it easier to read
         x = -6

Check your answer by plugging -6 in for the x in the original problem:

$\frac{2}{3} - \frac{1}{x} = \frac{5}{6}$   Plug in -6 for x
$\frac{2}{3} - \frac{1}{-6} = \frac{5}{6}$   Change $\frac{2}{3}$ to $\frac{4}{6}$ so all denominators are the same
$\frac{4}{6} - \frac{1}{-6} = \frac{5}{6}$   Change $\frac{1}{-6}$ to  $\frac{-1}{6}$ for easier work
$\frac{4}{6} - \frac{-1}{6} = \frac{5}{6}$   Subtract the numerators (4 - (-1) )
$\frac{5}{6}$ = $\frac{5}{6}$

So, x = -6 .