# Inequality with absolute values

• November 15th 2010, 01:48 AM
WeeG
Inequality with absolute values
hi guys,

how do you solve this inequality ?

|x| + |x-1| < 5

thank you
• November 15th 2010, 01:58 AM
Prove It
You probably need to use the Triangle Inequality.

$\displaystyle |a + b| \leq |a| + |b|$.

So that means $\displaystyle |x + x - 1| \leq |x| + |x - 1|$

$\displaystyle |2x - 1| \leq |x| + |x - 1|$.

And since $\displaystyle |x| + |x - 1| < 5$ that means

$\displaystyle |2x - 1| < 5$.

Can you go from here?
• November 15th 2010, 02:23 AM
WeeG
yeah, cheers !
• November 15th 2010, 06:29 AM
Stuck Man
I was doing a similar question. What is the solution set of mod(2x+5) <= mod(x+1) ? I think it is {x: x=-2, x=4}. The question actually asks for the interval and gives the answer [-4,-2].
• November 15th 2010, 08:35 AM
Stuck Man
The answer is correct. Both sides of the equation can be squared to find the soloution. I have done it now.