Spurious Extraneous solution: solving absolute value

In mathematics, an extraneous solution (or spurious solution) is a solution, such as that to an equation, that emerges from the process of solving the problem but is not a valid solution to the problem.

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I am puzzled by how the spurious solution is introduced. 

When you draw lines. It means y = x + 1, y = 2x + 5, y = - 2x - 5. 

Can you see negative -4 is an invalid solution and -2 is the answer? You can't. 

When you draw lines. The equation really means y = x + 1, y = -x =1 and y = 2x + 5. 

Then the absolute sign makes the -negative value invalid  (That is, two lines below y-axis do not exit, marked as green). 有两条线组成。因为是绝对值，那么负值就不可能有解。or  "2x + 5" must be a positive number

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