# Homework Help: Absolute graphs

1. May 22, 2010

### SyNtHeSiS

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

Sketch the graph of y = 2|x - 1| - 3|x + 1| + 3x + 1, and hence solve the inequality 2|x - 1| - 3|x + 1| + 3x + 1 < 0

2. Relevant equations

None

3. The attempt at a solution

(Refer to attachment).

I dont know where (or if) I made a mistake, cause when I try drawing the graph, it looks nothing like the answer.

2. May 22, 2010

### annoymage

try to consider when x=2 , x=0.5, x=-2 and see what happen

3. May 22, 2010

### The Chaz

To generalize, think of the PIECEWISE defined function.
|x-1| is defined differently "to the left of x = 1" than it is "to the right of x = 1".
|x+1| ................................. x = -1

So when x is less than -1, |x+1| = -(x+1) and |x-1| = -(x-1).
If you don't understand the previous sentence, review the definition of the absolute value function and piecewise functions.

Having discussed what happens when x < -1, now let's consider when x is greater than or equal to -1. "Things change" (i.e. the piecewise abs definitions) when x = 1, so let's consider the interval [-1, 1).
On this interval, |x-1| = -(x-1) and |x+1| = (x+1).

What happens on [1, inf) ??

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