# Solve for r - inequality

1. Mar 11, 2013

1. The problem statement, all variables and given/known data

|4 + 2r - r^2| <1

2. Relevant equations

4 + 2r - r^2 = (r - (1+ √5) ) (r - (1 - √5))

3. The attempt at a solution

I tried to use the roots but no use. How should I proceed?

2. Mar 11, 2013

### tia89

First of all you have to take away the absolute value... this means that you have to solve a system of inequalities.
Indeed if the quantity in the abs val is negative, then you will have to change sign, and if it is positive you can take away the abs val without problems.

As an example, in general when you want to solve $|x|<a$ you do the following:
solve
$$\begin{cases} x\geq 0 \\ x<a \end{cases}$$
Then solve
$$\begin{cases} x<0 \\ -x<a \end{cases}$$
(this because in case x is negative then you can take away the abs val but you have to change sign)
When done, just combine the solutions and you are done

3. Mar 11, 2013

### Ray Vickson

Start by drawing a graph of the function f(r) = 4 + 2r - r^2.