1. Solving equations tutorial. A small set of problems to help you clearly see the steps involved in solving equations: a) simplify both sides to get rid of any parentheses b) gather all ‘x’ terms on one side of the equation and all constant terms on the other and c) divide both sides by the coefficient of the ‘x’ term.

To do so, you have 4 tools - addition, subtraction, multiplication and division – and you can use those tools in any order as long as you treat both sides of the equation the same.

There are two special cases showing what happens when an equation doesn’t have a solution, or when any number plugged in for x is a solution. I ask you to figure out which is which.

The last 2 equations ask you to clear the fractions first by multiplying both sides of the equation by a common multiple of all the denominators.

2. Converting Units. A free-form tool that shows you how you can cancel units when you multiply fractions. Here’s what you need to know to use it:

1. Any fraction where the numerator is equivalent to the denominator can be treated as “1”.This is called a unit fraction .
   For example, if gas costs $4.38 per gallon, we can say $4.38 is equivalent to one gallon of gas, and $4.38 over 1 gal is a unit fraction. Likewise, 1 gal over $4.38 is also a unit fraction.


2. When you multiply something by a unit fraction, you don’t change its basic value, but you can cancel out units to change how that value is expressed.
   For example, if you just spent $30 on gas, you can multiply the $30 by the unit fraction ‘1 gallon over $4.38’. This lets you cancel out the $ signs and ‘convert’ $30 into gallons. $30 is equivalent to 6.85 gallons.