When we have solved two-step linear equations previously, we have been applying properties of equality in order to isolate the variable (get it by itself). Here are those properties again
PROPERTIES OF EQUALITY
1. Addition/subtraction property: If a=b then a+c=b+c and a-c=b-c
2. Multiplication/division property: If u = b then c-a=c-b and
ab
(as long as e *0).
We want to use these properties when variables are on both sides of the equation. They give us
permission to add, subtract, multiply and divide both sides of the equation in order to isolate the
variable.
Exercise #2: Let's revisit the equation 5x + 6 = 2x +30. We will now isolate the variable.
(a) The first two steps would be the following:
5x + 6 = 2x + 30
- 6= -6
5x = 2x + 24
- 2x = - 2x
3x =24
What property justifies both steps?