Question

I am having problems with variables on both sides. I get most of the concepts but I need help with adding fractions into the equations.

Answer 1

There are two ways for dealing with fractions in algebraic equations.

1. Multiply the whole equation with the LCM (lowest common denominator) of all fractions. This will then give you a whole number equation to work with.

Example: 1/2 x - 4 = 2/3 x + 5/6

Multiplying with the LCM of 6 gives

6*(1/2 x) - 6*4 = 6*(2/3 x) + 6*(5/6)

or 3x - 24 = 4x + 5

then solve as normal to get x = -29

2. Leave the equation as it is and work as you always do. Let's use the same example:

1/2 x - 4 = 2/3 x + 5/6

Work as always to collect the variables on one side and the non-variable terms on the other. I will do this here by subtracting 1/2 x from both sides and by subtracting 5/6 from both sides. That gives

-4 - 5/6 = 2/3 x - 1/2 x

or -4 - 5/6 = (2/3- 1/2) x

Now again, you will need to use the LCM (although here you just need to find the LCM of the fractions you actually want to add/subtract; coincidentally this is also 6, but you may, in other problems, find smaller LCMs)

with a common denominator you get

- 24/6 - 5/6 = (4/6 - 3/6)

or -29/6 = 1/6 x

Divide both sides by 1/6 and you get

-29 = x