how would you solve this problem?

draw a picture

By solving it ;)

With mathematics

you just gotta do the math

>>8733106
You set up four equations

|x+2| - |x-4| = 2
|x+2| = 2 + |x-4|

The second equation implies that

x+2 = 2 + |x-4| or x+2 = -2 - |x-4|

Then |x-4| = x +2 - 2 or |x-4| = -2 - x - 2
So |x-4| = x or |x-4| = -x - 4

So x-4 = x or x-4 = -x or x-4 = -x - 4 or x -4 = x + 4

So -4=0 or 2x = 4 or 2x = 0 or -4 = 4

So x = 4/2 or x = 0/2.

So x = 2 or x = 0 are your possible solutions

Now plug them back in to verify if they are correct

Notice that x = 0 is not a valid solution, so x = 2 is your only good solution

File: sci1.jpg (75KB, 750x1334px) Image search: [Google]

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>>8733124

File: sci2.jpg (75KB, 750x1334px)

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>>8733132

File: sci3.jpg (77KB, 750x1334px)

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>>8733134

I'd look at it for two seconds and see X = 2 because I'm not a computer and can use my intuition sometimes.

on (-inf,-2): -x-2-4+x = 2; no solutions since -6=/=2
on [-2,4): x+2-4+x=2 <=> 2x-2=2 <=> 2x=4 <=> x=2
on (4,inf): x+2-x+4=2 <=> 6=2

x=2 is the only solution

>>8733435
make that [4,inf)

>>8733106
Suppose x < -2. Abs goes away. See which x works (or not).
Suppose -2 x < 4. Abs goes away (differently though.) See what works.
Suppose x > 4, same thing.

Then conclude.

File: reeeeee.png (51KB, 1566x666px) Image search: [Google]

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don't make it harder than you need, just draw a graph

dist(x,-2) - dist(x,4) = 2
dist(x,-2) = 2 + dist(x,4)
x is 2 units further from -2 than it is from 4
midpoint(-2,4) = (-2 + 4)/2 = 1
going 1 unit closer to 4 from the midpoint
(and thus also 1 unit further from -2),
gives 2.