Introduction. This is one of the hardest topics. Therefore I figured out two tricks they are very easy and they work most of the time.

1. The "Common Sens" Approach (1st trick).
E.g. Solve this equation:

To solve an equation means to find a value of the variable (in one case "x") that makes the statement true. You should say to yourself:

so that something must be 42. Therefore, 3x = 42, which means 3 times something = 42. So it must be

So x = 14. In other words don't think of it as algebra, but as "Find the mystery number".

2. The Trial and Error Method (2nd trick).
This is a perfectly good method, and although it won't work every time, it usually does, especially if the answer is a whole number. The big secret of trial and error method is to find two opposite cases and keep taking values in between.
Solve for x :

Find a number that makes Right Side (RS) bigger, and then one that makes the Left Side (LS) bigger, and then try values in between them.

1 st case try a number that makes RS bigger:

2nd case try a number that makes LS bigger:

3rd case try in between:

Overall there are six steps to solve any type of equations:
To illustrate the sequence of all possible steps I am going to use a hard example (radical equation):

2nd STEP. Get everything off the buttom by cross - multilping up to every other term: (L.C.D.)

3rd STEP. Multiply out any brackets by using distributive properly:

4th STEP. Collect all uke term on the one side of the "=" and non-subject terms (constant terms) on the other side, remembering to remove the +/- sign of any term that crosses the "=" sign.

+18x moves across the "=" and becomes -18x;
+10 moves across the "=" and becomes -10;
-4 moves across the "=" and becomes +4

5th STEP. Combine together like terms on each side of the equation, and reduce it to the form "Ax = B"

6th STEP. Finally to get x = B/A divide both sides by A in our case by -15.

Example 1: By using the rules we set the (Simple Equations) variable terms on one side of the equation and the constant terms on the other side.

-9 moves across the "=" and becomes +9

Check	L.S. = x - 9
	L.S. = 44 - 9
	L.S. = 35
	L.S. = -421

L.S. = R.S. therefor 44 is the solution of the equation.

Example 2: (Solving Equations by Addition and Subtraction)

Again we set the variable terms on one side of the equation and the constant terms on the other side.
+4x moves across the "=" and becomes -4x
+54 moves across the "=" and becomes -54

Example 3: (Solving Equations by Division)

First multiply out any brackets by using distributive property:

Then get the variable terms on one side of the equation and the constant terms on the other.
+3x moves across the "=" and becomes -3x
-8 moves across the "=" and becomes +8

Example 4: (Solving Equations by Division)

Distributive property

Set the variable terms on one side of the equation and the constant terms on the other.

Colect like terms

Example 5: (Solving Equations by Multiplication)

First, set everything off the bottom by cross - multiplyng up to every other term (The L.C.D. for 3 amd 2 is 6).

Example 6: (Solving Equations Involving Polynomials)

Foil

Remove brackets by using distributive property

Set the variable terms onone side of the equation and the constant terms on the ither side.