No matter how simple or how complex an equation is, the equation is solved by following the equation solving questions.

Equation solving questions:

1. Can I simplify?
2. Did they add or subtract
   they refers to whoever made up the equation
3. Did they multiply or divide?

A basic property of equation solving is: what you do to one side of an equation, you must do to both sides. If we do the same operation to both sides of an equation, the result is an equivalent equation.

Equivalent equations are equations that have the same answer.

To solve any equation, you must isolate the variable on one side of the equation. That is, one side of the equation must contain only the variable with a coefficient of one.

So we will always solve for a +1 on the variable. Remember that 1x = x and we will not write a coefficient of one.

To solve equations that involve addition or subtraction, we will rewrite the equation leaving some space between the left-hand side of the equation and the equal sign.

Always look at the number of the side of the variable.

Examples:

1.	a - 5 = 7	Reasoning:
	a - 5      = 7	Look at the number with the variable -5. They have subtracted 5 so we rewrite and leave some room.
	a - 5 + 5 = 7 + 5	To cancel the -5, we add 5 to both sides.
	a = 12	Simplify: -5 + 5 = 0 and 7 + 5 = 12

2.	-5 = -3 + x	Reasoning:
	-5      = -3 + x	Look at the number with the variable -3. They have subtracted 3 so we rewrite and leave some room.
	-5 + 3 = -3 + x + 3	To cancel the -3, we add 3 to both sides.
	-2 = x	Simplify: -5 + 3 = -2 and -3 + 3 cancel leaving x

In the two samples above, and in the next samples, the first and second equations can be written as one step. I have shown them as two steps here only to show you what I mean by rewriting and leaving some room.

3.	a + 7 = 3	Reasoning:
	a + 7      = 3	Look at the number with the variable +7. They have added 7 so we rewrite and leave some room.
	a + 7 - 7 = 3 - 7	To cancel the +7, we subtract 7 from both sides.
	a = -4	Simplify: +7 - 7 cancel leaving a and 3 - 7 = -4

4.	8 = a + 3	Reasoning:
	8      = a + 3	Look at the number with the variable +3. They have added 3 so we rewrite and leave some room.
	8 - 3 = a + 3 - 3	To cancel the +3, we subtract 3 from both sides.
	5 = a	Simplify: 8 - 3 = 5 and 3 - 3 cancel leaving a

We can also check our answers to make sure we have worked our problems correctly. To do so, substitute the answer for the variable in the original problem.

Examples:

1.	a - 5 = 7	Reasoning:
	a - 5      = 7
	a - 5 + 5 = 7 + 5
	a = 12
Check	12 - 5 = 7	Substitute the 12 for x and simplify
	7 = 7

We must remember that when solving equations, we always solve for +1 on the variable. If the variable is negative, we must change it to positive and what we do to one side, we must do to both sides. So we must change the sign of the numbers as well.

Examples:

1.	5 - x = 7	Reasoning:
	5 - x      = 7	Look at the number on the side of the variable 5 They have added, so we rewrite and leave some room
	5 - x - 5 = 7 - 5	To cancel the 5, we subtract 5 from both sides
	-x = 2	Simplify 5 - 5 cancel leaving -x and 7 - 5 = 2
	x = -2	We do not want -x so we change it to x and what we do to one side we must do to both sides so change the 2 to -2
Check	5 - -2 = 7	Substitute the -2 for x
	5 - (-2) = 7	We can not have two minus signs in a row, so we must put the -2 in ( )
	5 + 2 = 7	The minus sign in front of ( ) tells us to change the sign
	7 = 7	Simplify: 5 + 2 = 7