The Distributive Property Lesson 25

Solve each equation. Check your solution. 1. 5x – 7 = – = –d = –12

Targets: Use the Distributive Property to simplify expressions. Solve equations using the Distributive Property.

 Term: A number or the product of a number and a variable.  Constant: A term with no variable.  Coefficient: The number multiplied by a variable.

For any numbers a, b and c: a(b + c) = a(b) + a(c) or ab + ac a(b – c) = a(b) – a(c) or ab – ac

Use the Distributive Property to simplify each expression. 7(x + 8) 7(x) + 7(8) 7x + 56 –3(y – 2) –3(y) – (–3)(2) –3y –(–6) –3y + 6

Use the Distributive Property to simplify each expression.

1. Distribute the front coefficient to remove the parentheses. 2. Undo addition or subtraction using inverse operations. 3. Undo multiplication or division using inverse operations. 4. Check your answer.

3(x + 5) = 33 3x + 15 = 33 –15 –15 3x = x = 6 3(6 + 5) ≟ 33 3(11) ≟ = 33 Solve the equation for the variable. Check your solution.

–5(2m – 1) = 25 –10m + 5 = 25 – 5 –5 –10m = 20 –10 –10 m = –2 –5(2(–2) – 1) ≟ 25 –5(–4 – 1) ≟ 25 –5(–5) ≟ = 25 Solve the equation for the variable. Check your solution.

Tiffany works as a travel agent. All the employees at her work are required to sell a certain number of vacation packages each day. Tiffany has sold 3 more than the required amount each day for the last 12 days. If she has sold 84 vacation packages, what is the required amount of packages that each employee must sell daily?  Equation: 12(v + 3) = 84  Distribute. 12v + 36 = 84  Subtract. –36 –36 12v = 48  Divide v = 4  Each employee must sell 4 vacations a day.

Use the Distributive Property to simplify each expression. 1. 3(x – 5) 2. –2(6x + 1) Solve each equation. Show your work and check your solution. 3. 8(x –1) = –20 = (6x + 2)

What steps would you take to solve the equation 4(x + 3) = – 8?