Absolute Value with two expressions.

[stuart4512]

How do I do this? I have tried a few methods and end up getting x values that don't work when placed back into the equation.

View attachment 3670

 

[MarkFL]

I would write the expression as a piecewise function:

$$f(x)=\begin{cases}-3x-5, & x<-1 \\[3pt] x-1, & -1\le x\le2 \\[3pt] 3x-5, & 2<x \\ \end{cases}$$

Can you proceed?

edit: I have moved this thread here from our Linear Algebra subforum, as this is a better fit. :D

 

[stuart4512]

I got the only solution to be at x=1.
How do I sketch the area between -1 and 2?

 

[MarkFL]

I got the only solution to be at x=1.
How do I sketch the area between -1 and 2?

You should find 2 valid roots. Check the root of each piece, and if it is in the given domain for that piece, then it is a valid root.

As for the middle piece, just compute the end points, and connect them with a line segment.

$$f(-1)=-2$$

$$f(2)=1$$

So, plot the points $(-1,-2),\,(2,1)$ and connect them.