A linear equation or first-degree in is written in standard form as
                                       With  
            This solved as follows:
                       
                           (We subtracted form both sides)
                            (We divided both sides by)
In many cases, simple first-degree equations can be solved mentally.
For Example, the solution of  is  and
                        the solution of  is  

Example:
            Solve the linear equation
Solution:
                     We have
           
               (We subtracted from both sides)
                        (We combined like terms)
                            (We subtracted from both sides)
                                 (We multiplied both sides by)
                                     (We divided both sides by)
                         
            To guard against errors in arithmetic or algebra, it’s a good idea to check the solution by substituting it back into the original equation. Thus, if we substitute in the equation, we obtain
           
                          Which shows that  is indeed the solution.

Example:
            Solve the linear equation
Solution:
            Multiplying both sides of the equation by the LCD and simplifying, we have
           
            that is,    or  
            Adding  to both sides of the last equation, we obtain
                        ;    that is    
            From which it follows that. We now check by substituting in the original equation to obtain
           
            an equation in which neither side is defined because of the zeros in the denominators. In other words, the substitution doesn’t make the equation true it makes the equation meaningless. Here, the correct conclusion is that the original equation has no root.