2
WORKING WITH THE DISTRIBUTIVE PROPERTY
Example: 3(2x – 5) + 5(3x +6) =
Since in the order of operations, multiplication comes before addition and subtraction, we must get rid of the
multiplication before you can combine like terms. We do this by using the distributive property:
3(2x – 5) + 5(3x +6) =
3(2x) – 3(5) + 5(3x) + 5(6) =
6x - 15 + 15x + 30 =
Now you can combine the like terms: Final answer:
6x + 15x = 21x 3(2x – 5) + 5(3x + 6) = 21x + 15
-15 + 30 = 15
Practice Examples:
Solving Equations
Golden Rule of Algebra:
“Do unto one side of the equal sign as you will do to the other…”
**Whatever you do on one side of the equal sign, you MUST do the same exact thing on the other side. If you
multiply by -2 on the left side, you have to multiply by -2 on the other. If you subtract 15 from one side, you must
subtract 15 from the other. You can do whatever you want (to get the x by itself) as long as you do it on both
sides of the equal sign.
Solving Single Step Equations:
To solve single step equations, you do the opposite of whatever the operation is. The opposite of addition
is subtraction and the opposite of multiplication is division.
Solve the following equations for x: