Download Solving Two Step Equations

Solving Two Step
Equations
August 19,2013
WELCOME!
Math is used in everyday life activities consciously and unconsciously.
Objective: The student will solve two step equations using the
addition, subtraction, multiplication, and division properties of
equality.
Students will identify the Commutative and Associative Property.
All students will be able to solve real-world application:
There are 26 students in Ms. Bean's class. The number of boys is
equal to seven fewer than twice the number of girls. How many
boys and how many girls are in the class?
Monday, Aug. 19
Round the decimals to the underlined place value.
1)
2)
3)
4)
5)
4.987
3.134
79.85
542.91
12.1052
4.99
3.1
80
540
12.105
Properties of Math
Commutative Properties of Addition and Multiplication
For any numbers a and b,
a+b=b+a
The order in which
numbers are added does
not change the sum.
9+2=2+9
For any numbers a and b,
a*b=b*a
The order in which
numbers are multiplied
does not change the
product.
6*5=5*6
Properties of Math
Associative Properties of Addition and Multiplication
For any numbers a, b, and c,
(a + b) + c = a + (b + c)
The way in which addends
are grouped does not
change the sum.
(5 + 3) + 1 = 5 + (3 + 1)
For any numbers a, b and
c,
(a * b) * c = a * (b * c)
The way in which numbers
are grouped does not
change the product.
(2 * 6) * 7 = 2 * (6 * 7)
Instruction
It takes two steps to solve an equation that has more than
one operation.
1.
Simplify by using the addition or subtraction
property of equality. (use the inverse of addition or
subtraction)
2. Simplify further by using the multiplication or
division property of equality. (use the inverse of
multiplication or division)
Consider the problem:
2x-15=5
Practice Problems
Let’s practice these problems as a group –
check answers with your table group
• 11n + 1 = 67
• -2y + 4 = 8
• 5x – 2 = 3
Steps
11n + 1 = 67
-1 -1
11n = 66
11
11
n=6
Subtraction Property of Equality
Division Property of Equality
Steps
-2y + 4 = 8
-4 -4
-2y = 4
-2 -2
y = -2
Subtraction Property of Equality
Division Property of Equality
Steps
5x – 2 = 3
+2 +2
5x = 5
5
5
x=1
Addition Property of Equality
Division Property of Equality
Challenging Practice Problems
Practice these problems with your table group
• 6 – 3y = -3
• 7 = 4 – 2y
• 3/2 = 5/2 + 7x
Steps
6 – 3y = -3
-6
-6
-3y = -9
-3 -3
y=3
Subtraction Property of Equality
Division Property of Equality
Steps
7 = 4 – 2y
-4 -4
3 = -2y
-2 -2
-3/2 = y
Subtraction Property of Equality
Division Property of Equality
Steps
3/2 = 5/2 + 7x
-5/2 -5/2 Subtraction Property of Equality
-2/2 = 7x
-1 = 7x
Division Property of Equality
7
7
-1/7 = x
90
80
70
Real World Situations
60
50
East
West
North
40
30
20
10
0
1st Qtr
2nd Qtr 3rd Qtr
4th Qtr
There are 26 students in Ms. Bean's class. The number of
boys is equal to seven fewer than twice the number of
girls. How many boys and how many girls are in the
class?
You are ordering tulip bulbs from a flowering catalog.
The cost is .75 cents per bulb. You have $14 to spend.
If the shipping cost is $3 for any size order, determine
the number of bulbs you can order.
Steps
x + 2x – 7 = 26 x is # of girls; 2x-7 is # of boys
3x – 7 = 26
+7 +7 Addition Property of Equality
3x = 33 Division Property of Equality
3
3
x = 11
So there are 11 girls and 15 boys.
Steps
.75b + 3 = 14
- 3 - 3 Addition Property of Equality
.75b = 11 Division Property of Equality
.75 .75
b = 14.667
So you can purchase about 14 bulbs. If you
purchase 15 bulbs you will go over your $14
budget.
What have you learned!!
Math is used in everyday life activities consciously and
unconsciously.
Objective: The student will solve two step equations
using the addition, subtraction, multiplication, and
division properties of equality.
All students will be able to solve: