2.1   Solving Equations      Homework: Odds 1 – 59

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DSPM 0800 Class Notes

Solving is finding replacements for the variable that will make a true statement.
Example:  x + 5 = 9
We can determine by inspection that 4 is the number that makes the equation true, so 4 is the solution of the equation.

Equations can be solved by a process of finding an equivalent equation in which the solution is obvious.
Example:  x = 3
The solution is obviously 3.
Notice: The most obvious equation to solve has the variable alone on one side of the equation.

The Process:
Add to or subtract from each side of the equation to get the variable term alone on one side of the equation only.
Divide or multiply each side of the equation to get the coefficient of the variable equal to one.

Example:  -6 = y + 25
              -6 – 25 = y + 25 – 25   Subtract 25 from each side to get variable alone.
                  -31 = y                  Simplify.

Now we can observe that the solution is –31. Check to verify!

Example:  100 = -x
               -100 = x     Divided each side by –1 to get the coefficient equal to 1.

Example:
                    
Multiplied each side by 5 to clear denominator. Divided each side by 4 to get the coefficient of the variable equal to 1.
Notice: These two steps could have been combined in one step by multiplying each side by the reciprocal of the coefficient, .
Observe that the solution is 20. 
Check:

Example: 
              Multiplied each term by 6 to clear denominators.
                    Canceled denominators.
                                 Simplified.
                         Subtracted 4 from each side.
                                      Simplified.
                                    Divided each side by 6 to get coefficient of 1.
                                       Simplified.

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