simplify x+3x

Question

i really dont know how to do it and i got mid terms this week

Answer 1

Let's consider a problem of adding apples and oranges.  If I have 3 apples and a friend gives you 2 more apples you have 3+2 = 5 apples.  Now let's say you have 3 apples and a friend gives you 4 oranges.  How many apples do you have?  You have 3 + 0 = 3 apples.  You cannot add apples and oranges together because they are two different things.  Now let's apply this to variables.  Let's say you have x and you want to add 3 more x.  You get 1x+3x = 4x.  You can just add the coefficients together because you are adding the same thing.  If the question was x+2y, these are different variables (adding apples and oranges) and cannot be simplified any further.

 

Now let's say I gave you an equation 3x +2y +6x + 10y, can you simplify?

Answer 2

Hi Alvis.

Ethan gave you the great explanation for understanding but I want to give you algebraic one.

You can rewrite the expression as 1×x +3×x. Now it looks like formula for distributive proprety

a×c - b×c=(a - b)×c

By applying distributive proprety you will get (1 + 3)×x = 4×x = 4x

This method only works if your terms have common variable, called like terms.

If you noticed: the coefitient in your answer is the sum of like terms coefitients.

Hope it helped.

Olga