# Simple Equations

A simple equation is equality, where one side of the equation is equal to the other side, in which the unknown has a  specific value. Therefore, an equation is a conditional value.

Thus, 3x = 12 is an equation since x has only one specific value, 4. But, there are 2 related topics that must be understood. before going deeper on learning how to solve an equation. Those topics are:

1) Equality - An equality in itself is a mathematical statement that shows two  equal expressions in value. There are three distinct characteristics in an equation, there are:

a) expression before the equal sign (=) is known as the left hand side of the equality

b) The equal sign (=), proving equality between 2 expressions.

c) The expression after the equal sign is known as right hand side of the equality.

Example:

2x = 4,    2y + 3y = 5y,     34 = 34

The above statements are all equalities.

2) Identity - An identity is also an equality, where letter or letters may have value, and is attributed to the identity. Therefore an identity is an unconditional identity.

Thus, 2y + 3y = 5y , x + y = y + x are identities since there is no specific values for x and y. X and Y can be any values satisfying the identity.

Any value that is satisfying an equation can also referred as  "solution to an equation". This solution is therefore any number which when replaced for the unknown, will make both side of the equation equal.

Example

Solve for X

2x - 4 = 0

Solution

Let isolate the 4, or move the 4 to the other side of the equation

2x = 4, or

x = 4/2. Therefore x = 2

Let check the equation, which is the process of replacing a value for an unknown to see if both sides are equal. In our case, replace x by 2 in the equation to see if there equality from both sides.

2x = 4, for x = 2

2 X 2 = , thus 4 = 4

Hence, 2 is a solution to 2x - 4 = 0,  since it satisfies the equation.

Example 2

Check the following equations

a) 4x - 7 = 3x  for x = 6 and x = 7

b) 2n + 3n = 25 for n = 5 and n = 6

a) Solution

Transpose 3x to the left side of the equation, and let the equation equals to 0

4x - 3x - 7 = 0

Let isolate the - 7

4x - 3x = 7, thus x = 7

Replace x by its value 6 and 7

If we replace x by 6, the equation cannot be equal

6 =7. Since 6 cannot be equal to 7. Thus, we have

6≠7 ( the reading is: 6 is not equal to 7)

Now if we replace by its real value 7, we now have:

7 = 7 (equality)

Thus 7 is a solution to 4x - 7 = 3x

b) Solution

2n + 3n = 25 for n = 5 and n = 6