Absolute value expressions written as piecewise expressions

i have to rewrite this as a piecewise expression : y=|6+2x|+1

i've gotten this far: positive case: y=6+2x+1 --> y=2x+7

negative case: y=-(6+2x)+1

y= -2x-5

so now what?

what is the actual piecewise expression and what is x > or < in each case and WHY?

i set the positive case to 0 for y and got x=-3.5 but the negative case to 0 for y gives x=-2.5

so is the final piecewise expression y={2x+7, x>=-3.5 ; -2x-5, x<=-2.5} ?

but that wouldn't necessarily make sense because they would overlap between -2.5 and -3.5

can someone please tell me what x is greater than or equal to and less than in the final piecewise function? and also where and WHY you got this?

If you draw f(x), you'll understand the solution!

Download Graph 4.4 from www.padowan.dk for free.

On "Function I Insert relation", type abs(6 + 2*x) + 1, then "OK".