1. Review of the Distributive Property of Multiplication Notes
What is the distributive property?
Distributive property – a mathematical property used to rewrite expressions involving addition or subtraction and multiplication.
Ex #1: a(b – c) rewrite as a(b + (-c)) a (b) + a (-c)
ab – ac
Ex #2: 2(x + 1) ∙x + 2∙ x + 2

2. Solving Linear Equations (isolate the variable)
Recall –
Solving Linear Equations (isolate the variable)
You must use the properties of equality to solve
an equation.
Ex #1 2x + 5 = 13
(subtract 5 from each sides)
2x = (divide each side by 2)
x = 4
Example #2
7x + 2 = 9x + 3
7x + 2 = 9x
-7x x (subtract 7x from each side)
2 = 2x (subtract 3 from each side)
-1 = 2x (divide each side by 2)
-1 = 2x
-½ = x

3. Multi-step equations (w/distributive property)
Use the distributive property
Example # (x + 5)
3(x) + 3(5)
3x + 15
Example #2 2(3x –10)
Rewrite as 2(3x + (-10))
2(3x) + 2(-10)
6x – 20
Example #3 -(x - 5)
Rewrite as (x + (-5))
-1(x) + (-1)(-5)
-1x + 5
Now, try these
-4(x – 4) b) 10(x + 10)
c) 7(x – 3) d) -(-x – 1)

4. Solutions to “Try These”
Now, try these
-4(x – 4)
Rewrite as -4(x + (-4))
-4(x) + -4(-4)
-4x + 16
10(x + 10)
10∙x + 10 ∙10
10x + 100
7(x – 3)
Rewrite as 7(x + (-3))
7 ∙ x + 7(-3)
7x + (-21) OR 7x – 21
d) -(-x – 1)
Rewrite as -1(-1x + (-1))
(-1)(-1x) + (-1)(-1)
1x OR x +1

5. Solving Multi-step Equations (isolate the variable)
Additional examples:
Ex #4 2g + 3(g + 1) = 13 (distribute 3 to everything in parenthesis)
2g + 3(g) + 3(1) = 13
2g + 3g = 13 (combine like terms)
5g = 13
(subtract 3 from each side)
5g = 10 (divide each side by 5)
g = 2
Ex #5 x + x + x + 3x = 24 (combine like terms)
6x = 24 (divide each side by 6)
x = 4

6. Vocabulary Terms
Distributive Property - a mathematical property used to rewrite expressions involving addition or subtraction and multiplication. Terms – the parts of an expression separated by addition or subtraction. Ex. 2x +3 ( 2x and 3 are the terms) Like terms – terms in an expression with the same variable raised to the same power. Ex. x3 + x2 + 3x3 (3x3 & x3 are like terms) Variable – a letter that represents an unknown number Properties of equality- whatever operation is done to one side of an equation must be done to the other to isolate the variable. Isolate – to get alone on one side of the equal sign. Equivalent Expressions - expressions of different forms that can be proven equal by substituting a number for the unknown. Ex. 4x + 4 , 4(x+1) and x + x +x +x + 4 are equivalent expressions