Graph & Solve Inequality: y = 2|x - 1| - 3|x + 1| + 3x + 1

[SyNtHeSiS]

Homework Statement

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

Homework Equations

None

The Attempt at a Solution

(Refer to attachment).

I don't know where (or if) I made a mistake, cause when I try drawing the graph, it looks nothing like the answer.

 

[annoymage]

Homework Statement

Sketch the graph of y = 2|x - 1| - 3|x + 1| + 3x + 1,

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

 

[The Chaz]

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

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) ??