Question

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

Answer 1

`(2)/(3) - (1)/(x) = (5)/(6)` Multiply both sides by 3

`2 - (1(3))/(x) = (5(3))/(6)` Simplify the numerators

`2 - (3)/(x) = (15)/(6)` Multiply both sides by 6

`12 - (3(6))/(x) = 15` Simplify the numerator

`12 - (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:


`(2)/(3) - (1)/(x) = (5)/(6)` Plug in -6 for x

`(2)/(3) - (1)/(-6) = (5)/(6)` Change
`(2)/(3)` to
`(4)/(6)` so all denominators are the same

`(4)/(6) - (1)/(-6) = (5)/(6)` Change
`(1)/(-6)` to
`(-1)/(6)` for easier work

`(4)/(6) - (-1)/(6) = (5)/(6)` Subtract the numerators (4 - (-1) )

`(5)/(6)` =
`(5)/(6)`

So, x = -6 .