Question

How do you solve the equation `abs(x-a)=b`?

Answer 1

`x={(a+b,color(white)("xxx"),"if " x>=a),(a-b,,"if "x < a):}`

Explanation:

This requires a piece-wise solution with the pieces dependant upon whether `(x-a)` is positive or negative.

`{: ("if " (x-a) >= 0,"then "abs(x-a)=x-a,rarr x-a=b" becomes " x=a+b), ("if "(x-a) < 0,"then "abs(x-a)=a-x,rarr a-x=b" becomes " a-b=x) :}`