1. Distributive Property, Combining Like Terms, Solving Equations with Variables on Both Sides

2. Distributive Property
An algebra property which is used to multiply a single term and two or more terms inside a set of parentheses.
2 (3 + 6)

3. 6(2+4x)
The two terms inside the parentheses cannot be added because they are not like terms. Therefore, 2 + 4x, the expression inside the parentheses, cannot be simplified any further.
Therefore, we must distribute the 6 across the parentheses!

4. -(3 + x2)
Change each positive or negative sign of the terms that were inside the parentheses. Negative or minus signs become positive or plus signs.

5. Try Some Yourself! 9(x + 9) 2(4 + 9x) 7(x + -1) 12(a + b + c)

6. Combining Like Terms Term
Number, variable, or product/quotient of numbers and variables (Ex: 5, m, 2x²)
Like Terms
Terms with the same variable AND exponent

7. Combining Like Terms
To simplify expressions with like terms, add or subtract the coefficients.
4k + 5k = 9k

8. Combining Like Terms
2ab + 6ba
Can you add the following?
3x³y + 2xy³

9. Try It Yourself! -x + 3y – 2x + y + 4 + 5x -1
5a – 3b + 12 – a + 3 – 14b
3x + 2m – 14x + 2x – 4m

10. Solving Equations with Variables on Both Sides
If you had this equation, how would you move  the 7 to the other side of the equation?
3x + 3 = x + 7

11. Exactly the same way you moved the seven!
How would you move the x from the left side to the right side?
3x + 3 = x + 7
Exactly the same way you moved the seven!

12. Once you subtract the x from both sides, the equation becomes a two-step equation!

13. Try This One on Your Own!
4x + 7 = 2x -1

14. Another One!
-2x – 10 = -9x + 11