Basic algebraic problem! can u help?

Question

determine if the statement is sometimes, always , or never true.

If a and b are real numbers, then | a +b | = |a| + |b|

i know that the answer is sometimes just that i don't know how to explain it. best answer i'll give 10 points please help

Answer 1

if a and b are both positive, then (a + b) is positive

so, | a +b | = |a| + |b|

if both are negative, say a = -A and b= -B, then

| a +b | = | -A - B| = |-(A+B)| = A + B

|a| + |b| = |-A| + |-B| = A + B

so, | a +b | = |a| + |b|

if either of them are negative, say a = - A and b = B, then

| a +b | = | -A + B| = |-(A-B)| = A - B

|a| + |b| = |-A| + |B| = A + B

so, | a +b | is not  |a| + |b|

Hence,  | a +b | = |a| + |b| is sometimes true. not always

Answer 2

easy...

the absolute value is always positive, right?

so either you solve it like this : |a+b|

or like this: |a| + |b|

you'll get the same answer...

ad its always positive...

Answer 3

try when a>b

then try numbers for when a<b

u will soon see yr answer

Answer 4

I a+ b I = I a I + I b I

lets say

a = -7

b = 3

I (-7) + 3 I = I -7 I + I 3 I

I (-4) I = 7 + 3

4 = 10

If one of the variable is negative:

It most likely won't work because on the right side, the numbers become positive before adding.

On the left side, you would need to add the two numbers together before taking the absolute value.

Lets say:

a = 3

b = 4

I 3 +4 I = I 3 I + I 4 I

I 7 I = 3 + 4

7 = 7

If both a and b are positive both sums are equal