I am interpreting yoru question as:
y = x +  x + 1
The absolute value of a number is either the number or its opposite, whichever is positive.
For x < 0, x = x. For x ≥ 0, x = x
Examples:
2 = (2) = 2
7 = 7
For your equation, you have x+1. When x + 1 < 0, x+1 = (x+1) = x1. When x+1 ≥ 0, x+1 = x+1.
x+1 ≥ 0 is the same as saying x ≥ 1.
x + 1 < 0 is the same as saying x < 1
So your equation could be described as two separate equations depending on what the vlaue of x is:
y = x +  x + 1
For x < 1:
y = x + (x+1)
or y = 1
For x ≥ 1:
y = x + x +1
or y = 2x + 1
To summarize:
y = 1 {x < 1} and y = 2x + 1 {x ≥ 1}
This is called a piecewise function since it is defined in pieces. All functions with absolute values can be turned into piecewise functions.
This graph should look like a steep upward climbing line to the right of x = 1 and a horizontal line below the y axis to the left of x = 1. At x = 1, the y value is 1 for both halves of the equation, so it is a continuous function.
I'm not sure where the question wants you to go with this since you are not given any y or x values to plug in and use to solve. Perhaps there is more to the problem you can add with the discussion feature.
10/16/2012

Robert C.
Comments
What is the problem asking you to solve for?