Real Numbers a, b, & c

[nycmathguy]

What on earth is this?

 

[MathLover1]

|a+b+c| ≤ |a|+|b|+|c|

hint: |a+(b+c)|

a,b, and c represent the sides of the triangle

Triangle Inequality states a < b+c
Triangle Inequality for Absolute Values states that |a|≤|b+c|

so,
|a|+|b+c| ≤ |a|+|b|+|c|............since |b+c|=|b|+|c|, we have

|a|+|b|+|c| ≤ |a|+|b|+|c|

 

[nycmathguy]

|a+b+c| ≤ |a|+|b|+|c|

hint: |a+(b+c)|

a,b, and c represent the sides of the triangle

Triangle Inequality states a < b+c
Triangle Inequality for Absolute Values states that |a|≤|b+c|

so,
|a|+|b+c| ≤ |a|+|b|+|c|............since |b+c|=|b|+|c|, we have

|a|+|b|+|c| ≤ |a|+|b|+|c|

Proofs are simply not for me, which explains why I didn't major in mathematics.