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# Help with modulus/inequalities question Watch

1. Given |x-2| + |x-1|>1, how do I find the values of x that satisfy this equation? I know the normal way of solving this is to square both sides, but that doesn't seem to work in this case. Thank you!
2. Draw a graph of y = |x - 2| and y = 1 - |x - 1|
That should make it easier.
3. (Original post by morgan8002)
Draw a graph of y = |x - 2| and y = 1 - |x - 1|
That should make it easier.
Okay, so it looks like it only holds for x<1 and x>1, but how do I prove this algebraically?
4. (Original post by thescottie)
Okay, so it looks like it only holds for x<1 and x>1, but how do I prove this algebraically?
When x<2, |x - 2| = 2 - x
When x>2, |x - 2| = x - 2

When x < 1, 1 - |x - 1| = 1 - (1 - x)
When x > 1, 1 - |x - 1| = 1 - (x - 1)

Use this information and the graph to find the points of intersection. Then use the graph to find the sign of each critical region.

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Updated: January 17, 2015
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