pre calc proof

[hagen19]

I'm having a hard time starting proofs. If you could help me start these proofs I'd appreciate it.

For Real number x that |x|=|-x|

and

For Real numbers if 0<a<b then a^2 < b^2

thanks!

 

[HallsofIvy]

I'm having a hard time starting proofs. If you could help me start these proofs I'd appreciate it.

For Real number x that |x|=|-x|

One of the things you need to learn about proofs is that you use the specific details of definitions. For example, the definition of "absolute value" is "if \(\displaystyle x\ge 0\) then |x|= x while if x< 0 then |x|= x. So do two cases: If \(\displaystyle x\ge 0\), what is |x|? What is |-x|? Then I x< 0, what is |x|? What is |-x|?

and

For Real numbers if 0<a<b then a^2 < b^2

thanks!

If 0< a< b, then b+ a> 0 and b- a>0. So what can you say about (b+ a)(b- a)?