1. The problem statement, all variables and given/known data [tex]|x + y + z| \le |x| + |y| + |z|[/tex]. Indicate when the equality holds, and prove your statement. 2. Relevant equations Answer in the books says it hold only when x, y, and z are all of the same sign. 3. The attempt at a solution The value on the rhs of the eq will keep getting bigger as the absolute value of x, y and z are added. It doesn't matter if x, y or z are positive or negative The value on the lhs will increase when the value of variable that is added is of the same sign and will decrease when the value is of the opposite sign. So lhs=rhs when the value of all variables are of the same sign and lhs<rhs when just one of the value are of a opposite sign.