$3x + 2 > 8$ solved not using order of operation? So im basically relearning algebra, using a site to teach myself the basics. I read about bodmas then shortly after about inequalities. In the practice questions i got a bunch of questions where the solution doesnt seem to use the order of operation, one being...
$$3x + 2 > 8$$
They first $-2$ from the $2$ then from the $8$. Then they divide the $3x$ by $3$ and the $8$ by $3$.
This confuses me because wouldn't you have to divide $\frac{3x}3$ then the same with the $8$ Before subtracting $2$ from the $2$ Then $8$? I don't know if im have a brain fart and missing a simple reason or maybe because its an inequality and nothing equals anything. Don't know.
So what i gather is that order of operations only really applies if there is an = sign in the equation? And that i could have divided by 3 but would have had to also divide the 2 by 3 along with the 8? which then leaves me with fractions and that just makes getting the solution a bit more complicated?
 A: *

*They probably divide the $6$ by $3$, since $6$ is what remains on the right side.

*You can first divide by $3$, of course, but you must always divide the whole equation, not only a number, so dividing by $3$ would give


$$\frac{3x+2}{3}>\frac83$$
which can be simplified into $$\frac{3x}{3} + \frac23 > \frac83$$
and further to $$x + \frac23 > \frac83$$
Then, instead of subtracting $2$ from each side, you can subtract $\frac23$ to get
$$x + \frac23 - \frac23 > \frac83 - \frac23\\
x + 0 > \frac{8-2}3\\
x > \frac63\\
x>2$$
A: The order of operations only comes into play when you're evaluating an expression: If you had to evaluate $3x + 2$ at $x = 2$, that is, simplify $3\cdot (2) + 2$, you would need the order of operations.
But when it comes to manipulating equations and inequalities, you don't need to do anything in any particular order (although some choices are easier than others, as the other answers have pointed out: subtraction first means you can avoid fractions). 
As long as you use valid algebra at each step (whether you subtract or divide first), you'll get the same solution.
A: You are correct that $3x+2 \gt 8 \iff x \gt 2$ (though you have since edited out the conclusion).  
If you divided by $3$ first you would get $x+\frac23 \gt \frac83$ reaching the same conclusion.
