M1A U1D4 Warm Up:
Write each phrase as an
algebraic expression.
1.
2.
3.
4.
$5 less than the original price.
9 more than 7 multiplied by g.
7 times the product of 15 and y.
22 less the quantity d and 35.
Warm Up:
Write each phrase as an
algebraic expression.
1.
2.
3.
4.
$5 less than the original price. p - 5
9 more than 7 multiplied by g. 7g + 9
7 times the product of 15 and y. 7(15y)
22 less the quantity d and 35. 22-35d
Homework Check:
Go over HW
Objective:
Students will be able to:
•Solve multi-step equations using
the Distributive Property.
•Have an understanding of what
property is used when solving
equations.
Properties...
Review the basic properties used
in mathematics.
Just watch…there’s a handout
coming!
Commutative Property:
The order in which numbers are
added or multiplied does not change
the sum or product.
a +b = b +a
and
a ∙b = b ∙a
Associative Property:
The way in which numbers are
grouped when added or multiplied
does not change the sum or product.
(a +b) + c = a +(b+c)
and
(a ∙b) ∙c = a ∙(b ∙c)
Additive and Multiplicative Inverses:
For every a, there is an inverse
(opposite operation).
a +(-a) = (a +-a) = 0
and
a ∙ (1/a) = (1/a) ∙a = 1
Distributive Property:
For any numbers a, b, and c:
a(b+c) = ab + ac and (b+c)a = ba + ca
a(b-c) = ab - ac and (b-c)a = ba - ca
Distribute Handout
Steps to Solving Multi-Step
Equations:
1. Distribute to clear parenthesis.
2. Combine like terms.
3. Use addition/subtraction to get the
variables on one side.
4. Add or subtract to isolate the variable.
5. Multiply or divide to isolate the variable.
Distribute Notes on
Multi-Step
Equations – Special
Cases
Complete together!
Additional Examples
Example 1:
Equations have one solution when the
variables do not cancel out. For example,
10x – 23 = 29 – 3x
+3x
+3x
13x - 23 = 29
+23 +23
13x = 52
13x = 52
13
13
x=4
Example 2:
Equations with no solution have variables
that will cancel out and constants that are
not equal. For example,
-x + 7 – 6x = 19 – 7x
-7x + 7 = 19 – 7x
+7x
+7x
7 ≠19
False therefore no solution!
Example 3:
An equation with infinitely many
solutions occurs when variables cancel out
and constants are equal. For example,
-1/2 (36a – 6) = ¾ (4 – 24a)
-18a + 3 = 3 – 18a
+18a
+18a
3=3
True therefore infinite solutions!
Additional Examples
Example 4:
A special equation with one solution when
the variables do not cancel out.
5x + 29 = 29 – 3x
+3x
+3x
8x + 29 = 29
-29 -29
8x = 0
8x = 0
8
8
x=0
Classwork:
Solving Multi-step
Equations Special
Cases #1-6 Handout
CW 2 :
Solving Multi-Step
Equations with
Distributive Property #1-6
Homework:
Kuta Multi-Step
Equations EVENS