Can Absolute Value Inequalities Prove This Expression?

[Andrax]

Homework Statement

we know that |a| < c and |bl < c
prove that : (la+bl + la-bl)/2 < c

The Attempt at a Solution

all I've gotten to so far is this : la+bl < 2c
lal + lbl < 2c
we have : la+bl < lal+lbl
then la+bl < 2c
i need to prove that la-bl < 0.?
also by squaring all i gotten so far is (la+bl + la-bl)/2 < 2c...

 

[tiny-tim]

Hi Andrax!

we know that |a| < c and |bl < c
prove that : (la+bl + la-bl)/2 < c

If they're complex, it's not true.

If they're real, then just try the 4 different ± possiblities,