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

Add 2n + 3n

5n = 25

If we replace n by 5, we now have:

5× 5 = 25

Therefore 5 is a solution to 2n + 3n = 25

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