Solving algebraic equations involves reversing (undoing) the order of operations. In order of precedence, the order of operations are parentheses, exponentiation, multiplication and division, and addition and subtraction. The order of operations can be remembered by the mnemonic PEMDAS. The reverse of multiplication is division (and vice versa) and the reverse of addition is subtraction (and vice versa).
I'll use the following equation as an example.
To solve the above equation in terms of , reverse the order of operations. First, subtract 5 on both sides of the equation to reverse the addition.
As you can see, the addition was undone by the subtraction. Now, divide by 2 on both sides of the equation to reverse the multiplication.
Reversing exponentiation involves a similar process. Take the following equation for example.
To reverse exponentiation, raise each side of the equation to the reciprocal power. The power is so the reciprocal is . Therefore, raise each side of the equation to 2nd power.
Remember the Laws of Exponents, specifically . Therefore, . As you can see, this undoes the exponentiation. Thus, we have:
Edit: Yes, nearly all if not all algebraic equations can be solved by undoing the order of operations.