1. The Distributive Property
Lesson 3
Linear Equations
The Distributive Property

2. Warm-Up State whether the equation is true or not with the
given values.
6x – 4y = 22 when x = 5 and y = 2
x + 5 = y when x = 6 and y = 11
y = – 3x – 1 when x = – 2 and y = – 7

3. The Distributive Property
Target:
Simplify expressions using the Distributive
Property and combining like terms.

4. Vocabulary Term: A number or the product of a number and a variable.
Constant: Term that has no variable.
Coefficient: The number multiplied by a variable in a term.
Distributive Property: A property that can be used to rewrite an expression without parentheses.
Like Terms: Terms that have the same variable raised to the same power.
Equivalent Expressions: Expressions that have the same value.

5. The Distributive Property
For any numbers a, b and c: a(b + c) = a ∙ b + a ∙ c a(b – c) = a ∙ b – a ∙ c

6. Example 1a
Use the Distributive Property to simplify each expression. 2(x + 6) 2(x) + 2(6) 2x + 12

7. Example 1b
Use the Distributive Property to simplify each expression.

8. Example 1c
Use the Distributive Property to simplify each expression. – 5(3x – 1) – 5(3x) – (– 5)(1) – 15x + 5

9. Example 2a
Find the product by using the Distributive Property and mental math. 4(103) 4( ) 4(100) + 4(3)

10. Example 2b
Find the product by using the Distributive Property and mental math. 998 ∙ 7 7(1000 – 2) 7(1000) – 7(2) 7000 –

11. Example 2c
Find the product by using the Distributive Property and mental math. 8(6.5) 8( ) 8(6) + 8(0.5)

12. Example 3
Simplify by combining like terms. 3x – 2y + 4 – 2x + x + 4y 2x + 2y + 4

13. Example 4
Simplify by combining like terms – 5(2x – 1) + 3x – 2 – 10x x – 2 – 7x + 3

15. Exit Problems Simplify each expression. 4(x − 3) 9x + 2 + 3x – 4 − 7x

16. Communication Prompt
How could the Distributive Property help you do mental
math in real-world situations?