Equations Involving Two Operation

Consider the equation 2x + 3 = 13. Note the left side of the equation involves the two operations of multiplication and addition. According to the order of operations, we should do the multiplication before the addition. We will always undo the operations in the reverse order from which we perform the operations. That is we undo the addition first, them undo the multiplication.

Usual Order of Operations	Order of Undoing the Operations
Multiply First	Subtract First to Undo the Addition
Add Second	Divide Second to Undo the Multiplication

Examples:

2x + 3 = 13          To undo the addition we subtract.
2x + 3 - 3 = 13 - 3  
2x = 10              To undo the multiplication we divide.
(2x)/2 = 10/2
x = 5


3x - 4 = 8           Note the operations involved on left side are multiplication and subtraction.
3x - 4 + 4 = 8 + 4   To undo this subtraction we add. 
3x = 12              To undo the multiplication we divide.
(3x)/3 = 12/3
x = 4


x/2 - 3 = 5           Note the operations involved on left side are division and subtraction.
x/2 - 3 + 3 = 5 + 3   To undo the subtraction we add.
x/2 = 8               To undo the division we multiply.
2(x/2) = 2(8)
x = 16


x/3 + 2 = 6           Note the operations involved on left side are division and addition.
x/3 + 2 - 2 = 6 - 2   To undo addition we subract.
x/3 = 4               To undo division we multiply.
3(x/3) = 3(4)
x = 12

Equations Involving Several Operation

More complex equations are generally handled as follows.

Clear fractions or by multiplying each side by the LCM of the denominators.
Simplify each side by performing indicated operations.
Add or subtract the same expression from each side to isolate variable on one side and constant on other.
Divide each side of the equation by the coefficient of the variable.

2(x/3 - 5) + x = x/2 - 3              Step 1:  Clear fractions 
                                      by multiplying each side by 6.

6[2(x/3 - 5) + x] = 6[x/2 - 3]        Step 2:  Simplify each side.
                                      Use distributive law.

12(x/3 - 5) + 6(x) = 6(x/2) - 6(3)    Applly distributive law again.

12(x/3) - 12(5) + 6x = 3x - 18.       Do indicated multiplications.

4x - 60 + 6x = 3x - 18                Combine like terms.

10x - 60 = 3x - 18                    Step 3:  Isolate variables by
                                      subtracting 3x from each side.

10x - 60 - 3x = 3x - 18 - 3x          Combine like terms.

7x - 60 = -18                         Add 60 to both sides.

7x - 60 + 60 = -18 + 60               Combine like terms.

7x = 42                               Step 4:  Divide each side by 7.

(7x)/7 = 42/7                         Simplify

x = 6

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