What Equation is?

An equation is a proposition, expressing in algebraic characters, the equality between one quantity or set of quantities and another, or between different expressions for the same quantity.

Any equation says: what is on the left of equal sign (=) is same as what is on the right of it.

-It says that two expressions on either side of the sign are equal

.-It is not an equation if there is a sign other than equality like greater than (>) and less than (<) in between expressions. They are called inequalities.

 If ‘>’ is used => L.H.S Expression value is more than R.H.S expression value.

If ‘<’ is used => L.H.S Expression value is less than R.H.S expression value.

If ‘≠’ is used => both expressions are not equal.

-Also an equation remains same though the both expressions are interchanged on either side.

E.g.  3x +6 = 21 ó 21 = 3x +6

        4y -2 = 30 ó 30 = 4y -2

Solving an Equation

An equation is said to be balanced when both sides of equality are equal.

                                  L.H.S = R.H.S

A balanced equation is like a weighing balance with equal weights on both its pans.

Properties of equality:

Addition Property:

 If same number is added to both sides of a balanced equation, then the balance is not disturbed.

a = b

a + c = b + c

Subtraction property:

If same number is subtracted from both sides of a balanced equation, then the balance is not disturbed.

a = b

a - c = b - c

Multiplication and division property:

 Similarly if same number is multiplied and divided on both sides of balanced equation, then the balance is not disturbed.

a = b

a x c = b x c

a ÷ c = b ÷ c

Source: Bhargavi Ramani, 12 June 2013, Text Section, Explaining properties of equality.

Solving equations using properties:

To solve basic algebraic equations of the form Ax=B is explained in following videos,

Video: http://www.youtube.com/watch?v=7T-_K_-VSJE

Video: http://www.youtube.com/watch?v=9Ek61w1LxSc

To check if a given value is a solution to an equation:

1. Evaluate the left-hand side expression at the given value to get a number. 
2. Evaluate the right-hand side expression at the given value to get a number.
3. See if the numbers match.

To solve for x in one step equations of the form

      X + a = b; where ‘a’ and ‘b’ can take any numerical value.

Solving one step equations by adding and subtracting whole numbers is explained in following video,

Video: http://www.youtube.com/watch?v=VidnbCEOGdg

Video: http://www.youtube.com/watch?v=yqdlj0lv7Cc

To solve for x in one step equations of the form

      X / a = b; where ‘a’ and ‘b’ can take any numerical value, is explained in following videos

Video: http://www.youtube.com/watch?v=rZuvbYO3sV8

 Video: http://www.youtube.com/watch?v=DqeMQHomwAU