When to switch from inequality to equality in substitution?

[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?

 

[Defennder]

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?

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.

 

[HallsofIvy]

"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.

 

[Moo Of Doom]

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