Solve 4x – 3 < 7?

You can treat inequalities the same as equalities (WITH ONE EXCEPTION which I'll get to later). Basically you can do whatever you want to one side of the sign, as long as you do the same to the other.

4x - 3 < 7
Add 3 to both sides.
4x < 10
Divide both sides by 4.
x < 10/4 (or 5/2 in lowest terms, or 2.5 in decimal form)

Easy as that.

The ONE EXCEPTION I mentioned is as follows: if you multiply or divide by a negative number, you must FLIP THE SIGN. For example:
-2x < 4
Divide both sides by -2, and the sign flips:
x > -2
(Find values for x that satisfy these inequalities and you will see that this is true.)

This is not an issue for your example but it is important to know.

4x – 3 < 7
4x < 10
x < 5/2 or x < 2.5

ADD 3 to both sides
4x -3+3 < 7+3
4x< 10
x<10/4
x< 5/2

x < 10/4

x < 5/2

X=2