General question, inequalities and graphing

[rocomath]

$$x+|x|=y+|y|$$

so for x which in a sense will be the same for y

x if x > 0
-x if x < 0

now does that only apply to my absolute x? or does it apply to both x and |x|?

 

[symbolipoint]

You should consider four sets of conditions: both less than zero, both greater than zero, one less and other greater; the other greater and the one less. An obvious solution is in case x=y=0, but you should check the other four conditions.

 

[rocomath]

no i meant if x < 0, then does it become

(-x) + (-x) or x + (-x)

does the condition only apply to the absolute value? but i checked my SM, i couldn't resist any longer :p

 

[symbolipoint]

Use a number line to justify this: but if x<0, then
$$\[<br /> x + \left| x \right| = x + ( - x)<br /> \]$$

 

[HallsofIvy]

$$x+|x|=y+|y|$$

so for x which in a sense will be the same for y

x if x > 0
-x if x < 0

now does that only apply to my absolute x? or does it apply to both x and |x|?

The trouble is you don't say what those two lines are EQUAL to. You should say "for x

|x|= x if $x\ge 0$
|x|= -x if x< 0.

Yes, of course, that applies only to the absolute value of x- it wouldn't make sense to say that x= -x! As symbolipoint said, you will have 4 cases to consider- the four quadrants- $x\ge 0$ and $y\ge 0$; $x\ge 0$ and y< 0; x< 0 and $y\ge 0$; x< 0 and y< 0.

 

[rocomath]

Use a number line to justify this: but if x<0, then
$$\[<br /> x + \left| x \right| = x + ( - x)<br /> \]$$

The trouble is you don't say what those two lines are EQUAL to. You should say "for x

|x|= x if $x\ge 0$
|x|= -x if x< 0.

Yes, of course, that applies only to the absolute value of x- it wouldn't make sense to say that x= -x! As symbolipoint said, you will have 4 cases to consider- the four quadrants- $x\ge 0$ and $y\ge 0$; $x\ge 0$ and y< 0; x< 0 and $y\ge 0$; x< 0 and y< 0.

Thanks! Unfortunately, I have another :p