The Degree Of An Equation

The degree of an equation describes what the highest power any variable in the equation is raised to.  A 1^st degree equation is used to describe an equation where the highest power of any variable is ‘1’.  A 2^nd degree equation is used to describe one where the highest power of any variable is ‘2’.  This goes on, for 3^rd degree, 4^th degree etc…

So take this equation for instance:

                                                          

There’s only one term in this equation which has a variable or pronumeral in it – the ‘x’ term.  Having just an ‘x’ there means it is raised to the first power, since we know that:

                                                            

So the equation is a first degree equation.  But what about this equation:

                                                

There are lots of terms in this equation, and two types of variable – ‘a’ and ‘b’.  The highest power of any ‘a’ is 3, and the highest power of any ‘b’ is 2.  Since a has the highest power, it determines what degree the equation is.  Because there is an ‘a’ raised to the power ‘3’, this means the equation is a 3^rd degree equation.

Solving first degree equations

Solving first degree equations is fairly easy, you just need to remember that whatever you do to one side of the equation you must do to the other side as well.  If you multiply one side by 5, you need to multiply the other side by 5 as well.  If you subtract ‘2x’ from one side, you need to subtract ‘2x’ from the other side as well.  Pretty easy stuff.  Here are the main things you can do to help you solve an equation:

·         Multiply or divide both sides of the equation by a number or pronumeral.

·         Add or subtract something from both sides of the equation.

·         Multiply out bracketed terms.

·         Make all fractions have a common denominator so you can do calculations with them.

·         Alternatively get rid of fractions entirely by multiplying both sides of the equation by the product of their denominators.

Remember that your final aim when you’re solving for the value of a particular variable or pronumeral is to get the equation in the form:

                                      

For instance, here’s a typical first degree equation:

                                                   

After a bit of practice with solving these, you should straightaway be able to notice that you can divide both sides by ‘4’:

                                                   

Now you can multiply out the brackets:

                                                     

Your end aim is to get “x = something…” At the moment, we’ve got terms with ‘x’ in them on both sides of the equation.  We can solve this by getting rid of the ‘x’ on the L.H.S. by subtracting ‘x’ from both sides:

                                                 

Now we’ve only got ‘x’s on one side of the equation, but we’ve also got a pesky ‘–9’ as well.  Let’s get rid of that by adding ‘9’ to both sides:

                                                    

Now the only thing we’ve got to do is get it down to only one x, we can do this by dividing both sides of the equation by ‘2’: