# Quick question about inequality notation

1. Aug 31, 2008

### quark1005

Which of the following is correct, if x = 4?

$$n\leq3x^{2}$$

$$\leq3(4)^{2}$$

$$\leq48$$

or

$$n\leq3x^{2}$$ $$=3(4)^{2}$$ $$=48$$

In other words, in what situations is it necessary to switch from inequality to equality, and it is always required to have only one comparison symbol per line?

2. Aug 31, 2008

### Defennder

It really depends on your writing style. Every maths textbook I've seen puts multiple comparison symbols per line, so it's not a big deal if you do so.

3. Aug 31, 2008

### HallsofIvy

Staff Emeritus
"A or B" is true if either A or B is true. In particular "$4\le 4$" means "4< 4 or 4= 4". Since the latter is true $4\le 4$ is true. Of course, it is more precise to say "4 = 4" but both are true.

4. Aug 31, 2008

### Moo Of Doom

Both of your examples are correct, but the second one is the one usually seen.