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SOLVING EQUATIONS WITH ONE VARIABLE

A) Simple Equations

Three steps to solve a simple equation:
1. Move all terms containing the unknow to the left side of the equation.
2. Collect like terms.
3. Divide by the coefficient of the unknown to get the answer.

Example 1: Solve  5x - 12 = 3x + 4

Solution: 5x -3x = 4 + 12
2x = 16
x = 8

Answer: x = 8

B) Equation with Fractions

Multiply both member of the equation for the Least Common Multiple among all denominators.

Example: Solve    

Multiplying by the LCD=30 we get:

C) Equation with Parenthesis

Remove the parenthesis performing the corresponding operations and proceed as in 1).

Example: Solve 3 – (2x – 3) = 6 + 3(x + 5)

3 – 2x + 3 = 6 + 3x + 15

-2x –3x = 6 + 15 – 6

-5x = 15

x = -3

  D) With Multiple Parenthesis

Remove parenthesis (using FOIL when applicable). Use auxiliary parenthesis for partial results., finally proceeds as in 3)  

Example: Solve 5 +(2x+1)(x+3) = 3x² –(x+3)(x+2)

5 + (2x² + 6x +x +3) = 3x² –(x² +2x+3x+6)

5 + 2x² + 6x +x +3 = 3x² –x² -2x-3x-6

2x² + 7x + 8 = 2x² -5x-6

7x + 5x = -6-8

12x = -14

x = -7/6

E) Fractional Type

Multiply the equation by the LCD Example: Solve

Multiplying by the LCD (x-3)(x+2) , we get

It's easy to check that x=4 satisfies the equation.

  F) Equation with Radical

Isolate the radical and then power both members of new equation to eliminate the radical.

Do not forget to check your possible solutions!

Example: Solve:

Isolating the radical we get:

Checking x=5, we get

So x=5 is the solution.

 F) Equation with no Solution

Example: Solve
Isolating the radical we get:


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