Distributive Property
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2-step equations with fractions & decimals
Solving equations with distributive property and CLT
Equation Grab-bag
Properties
100
5(x - 12)= -80
What is x = -4
100
Which of the 4 terms below can be simplified?
a. 3x^2 + 7x
b. -9p+ 12p
c. 2y - 4
d. 4x + 4y
What is b
100
What are the two steps in solving a two-step equation?
1. add/subtract on both sides
2. multiply/divide on both sides
100
10(w + 5) = -10
W = -6
100
What do the properties of equality state?
Whatever you do to one side of the equal sign, you have to do to the other (add, subtract, multiply, or divide)
100
What does the Commutative Property of addition and multiplication allow you to do?
Change the order to make adding and multiplying easier
200
7(m - 11) -7 = -98
m =-2
200
You rent a canoe for $7.50 per hour that has an initial cost of $20. You spend $57.50. How long did you rent the canoe for?
What is 5 hours
200
12.2 = 2x - 7.8
x = 10
200
10a + 6(a - 3) = -66
A = -3
200
11p = -44
What property of equality would you use to isolate the variable?
P.O.E multiplication
200
What does the Associative Property of addition and multiplication allow you to do?
Change the grouping to make addition and multiplication easier
300
2(t + 4) + 6t= 24
What is t = 2
300
Simplify the expression
6(c - 5) - 3c
3c - 30
300
If the area of the rectangle below is
87cm^2
Solve for X
x = 9
300
Solve the equation below and justify the steps by stating the properties of equality.
3/4x + 6 = 18
x = 16
P.O.E subtraction
P.O.E. Multiplication
300
What are the other four words that mean the same as multiplicative inverse
Multiply by the Reciprocal
400
-9(m - 4) - 9 =54
m = -3
400
What are the four steps in solving a multi-step equation?
1. Distribute
2. Combine Like Terms
3. add/subtract on both sides
4. multiply/divide on both sides
400
-3/4x + 7 = -8
x = 20
400
If the perimeter of the shape below is 52 ft, what is the length of the rectangle?
23 ft
400
Six more than the number w is 2
WRITE and Solve the equation
w = -4
400
What does it mean to distribute and give an example of a problem you would need to distribute
Multiply the outside number to everything inside the parentheses
3(x + 2)
500
- (-x + 9)= 4
x = 13
500
4/3w - 12 = 2/3w
w = 18
500
The cost (in dollars) of making n birthday cakes is represented by c = 30n + 25. How many birthday cakes did you make if the cost is $295?
x = 9 birthday cakes
500
A rectangle has the length of (x + 5)in and the width of 2in. The area of the rectangle is 60 inches squared. What is the length of the rectangle? A=LW
L = 30 in
500
What are the five steps in solving an equation with variables on both sides of the equal sign?
1) Distribute
2) Combine Like Terms
3)add/subtract coefficient
4) add/subtract constant
5) Multiply/divide to isolate the variable
500
What terms can be combined in the following expression:
-2x + 5x^2 -3x + 7y - 2
-2x and -3x which = -5x