Name: ______Per.: ______Date: ______

Linear Equation Day 12a: Solving Rational Equations That Involve Distributive

Property Part 2

DO NOW: Use the distributive property to simplify the expression and solve the equation.

1) -5(n – 10) / 2) 6 – (x – 3) = 7(x - 2) - 1

OBJECTIVE: By the end of this lesson, I should be able to ______

______

DEMO #1: Distributive Property

Key words to identify use of the distributive property.

Examples:

1)  Three times the sum of a negative number and eight______

Simplify:

Your turn:

2)  Twice the sum of ten and a negative number______Simplify:

It is not always going to be that simple

3)  Half the sum of six and a negative number, less four ______

Simplify:

Your turn:

4)  Two-third the sum of a negative number and nine, minus two ______

Simplify:

Let’s look at subtraction.

5)  Four times the difference between one half and a number ______

Simplify:

Your turn:

6)  Triple the difference between a negative number and one fourth ______

Simplify:

It is not always going to be that simple

7)  One-third the difference between 6 and a negative number, plus 8

Simplify:

Your turn:

8)  One-fourth the difference between 16 and a negative number, plus 3

Simplify:

DEMO #2: Solving Equations that use the Distributive Property.

1) Write an equation to represent the relationship. Then solve the equation.

Twice the difference of a number and ten is equal to twelve decreased by six times a number.

Your turn:

2) Double the difference of a number and six is the sum of ten and the number.

3) Five times the difference of six and the product of two and a number equals ten.

How else can we use the distributive property to solve problems?

Remember this problem?

4) The triangles shown have the same perimeter. What is the value of x?

Write an equation using the distributive property and solve.

Your turn:

3) Write an equation using the distributive property and solve. Remember this problem?
Claire purchased just enough fencing to border either a rectangular or triangular garden, as shown, whose perimeters are the same. How many feet of fencing did she buy? Write an equation and solve.

Closure:

In which of the following word problems would you use the distributive property?

1: Four more than one-half a number is the same as the difference between twenty four and two times the number.

______

2: One-fourth the sum of eight and twelve plus six is the same as one-half a number times two. ______

HOMEWORK:

1) 8 +2(p - 12) = p + 40 / 2) 10 -(5x - 36) = - (50 + 7x)
3) -3(4b – 10) = ¾ ( - 24b + 60) / 4) ½(2n – 6) = 4(n - 1)

Write an equation using the distributive property and solve.

5) Half the sum of six times a number and eighteen is the same as twice the number less twenty.
6) Triple the difference between a negative number and nine, plus nine equals the product of six and the negative number.
7) A square has sides which are five times a number plus three inches. The perimeter of the square is 72 inches. What is the length of each side?
8) The length of a rectangle is twice the sum of the width and five inches. The perimeter is fifty inches. What are the dimensions of the rectangle?

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