[tex] \frac{2}{3} - \frac{1}{x} = \frac{5}{6} [/tex] Multiply both sides by 3
[tex]2 - \frac{1(3)}{x} = \frac{5(3)}{6} [/tex] Simplify the numerators
[tex]2 - \frac{3}{x} = \frac{15}{6} [/tex] Multiply both sides by 6
[tex]12 - \frac{3(6)}{x} = 15[/tex] Simplify the numerator
[tex]12 - \frac{18}{x} = 15[/tex] 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:
[tex] \frac{2}{3} - \frac{1}{x} = \frac{5}{6} [/tex] Plug in -6 for x
[tex] \frac{2}{3} - \frac{1}{-6} = \frac{5}{6} [/tex] Change [tex] \frac{2}{3} [/tex] to [tex] \frac{4}{6} [/tex] so all denominators are the same
[tex] \frac{4}{6} - \frac{1}{-6} = \frac{5}{6} [/tex] Change [tex] \frac{1}{-6} [/tex] to [tex] \frac{-1}{6} [/tex] for easier work
[tex] \frac{4}{6} - \frac{-1}{6} = \frac{5}{6} [/tex] Subtract the numerators (4 - (-1) )
[tex] \frac{5}{6} [/tex] = [tex] \frac{5}{6} [/tex]
So, x = -6 .
