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

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)

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!

-(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.

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

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

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

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

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

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

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!

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

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

Another One! -2x – 10 = -9x + 11