Objectives 

• Linear Equations

• Equations with variables in a denominator

Examples

• Example 1

• Example 2

• Example 3

• Example 4

Find all real solutions (if any) for the given equation:



Solution:

Our goal is to "isolate the x."

    Step 1: Multiply out each side of the equation.



    Step 2: Combine like terms where possible on each side of 
                   the equation.



    Step 3: Subtract "6x²" from each side of the equation.





     Step 4: Add "13x" to each side of the equation.





     Step 5: Subtract 2 from each side of the equation. 





      Step 6: Divide each side of the equation by  - 11.





Our work demonstrates that the original equation will yield a true statement provided the variable "x" is assigned the number 
value 7/11. 

Note: As you become more practiced at solving equations, you can begin to combine some of the arithmetic steps listed above.

But be careful: Remember that in order to move an expression from one side of the equation to the other, you must perform the same arithmetic operation on both sides of the equation.