Question

How do you solve `abs(x-1/3)-2=1?`?

Answer 1

`x=10/3` or `-8/3`

Explanation:

As `|x-1/3|-2=1`, we have

`|x-1/3|=1+2=3`

hence either `x-1/3=3` i.e. `x=3+1/3=10/3`

or `x-1/3=-3` i.e. `x=-3+1/3=-8/3`

Graphically this solution can be plotted as the intersection points of the functions on the LHS and the RHS as shown below :-

Answer 2

`x_1 = 10/3`
`x_2 =-8/3`

Explanation:

Any algebraic problem with absolute values you always have to isolate the absolute value on one side of the equation.

In this case:

`|x-1/3| = 3`

remember that for absolute values you will have 2 answers because both positive and negative values have a positive absolute value:

`+-(x-1/3) = 3`

Solve for x:

`x_1 = 10/3`
`x_2 =-8/3`

Graphically this solution can be plotted as the intersection points of the functions on the LHS and the RHS as shown below :-