|x-1/5|= 3

For absolute equations, you actually have two equations you are solving for:

x - 1/5 = 3

and -(x - 1/5) = 3. There you have a negative outside the parentheses, that means you have to just switch the signs around in the parenthesis (aka multiply by -1).

So you would end up with -x + 1/5 = 3.

So your two equations to solve for x are:

x - 1/5 = 3 and -x + 1/5 = 3.

To solve the left equation, add 1/5 to both sides:

x = 3 + 1/5 But you need to change the fractions to get an answer.

x = 15/5 + 1/5

x = 16/5 this is your first answer.

Now solve the second equation: -x + 1/5 = 3.

It's pretty much the same thing: except you subtract 1/5 from both sides.

-x = 3 - 1/5

now change the fractions

-x = 15/5 - 1/5

-x = 14/5

x is negative (or multiplied by -1) so in order to find positive x, you need to divide both sides by -1, or just change the signs.

So you end up with:

x = 14/5

and you are done! :)

## Comments

first, for |x| = 3, we have x = (+/-)3; so, therefore, by analogy, |x - 1/5| = 3 means that x - 1/5 = 3, or x - 1/5 = -3; in either case, add 1/5 to each side of the equation; in the first equation, we then get x = 3 + 1/5 = 15/5 + 1/5 = 16/5; and in the second equation, we get x = -3 + 1/5 = -15/5 + 1/5 = -14/5