1. 3-1 Solve One Step Equations
Objective: Students will create and solve equations in one variable.
Standards: A.REI.3 , A.CED.1 , A.REI.1

2. Vocabulary Inverse Operations: Two operations that undo each other.
Examples: Addition & Subtraction
Multiplication & Division
Equivalent Equations:
Equations that have the same solution(s).

3. Example 1 Solve: x + 9 = 3 -9 -9 x = -6 Isolate the variable.
Get x by itself by doing the opposite operation.
What you do to ONE SIDE, you must do to the OTHER SIDE of the equation to keep it balanced.
x = -6

4. x = 13 x - 2 = 11 x – 2 = 11 +2 +2 Example 2 Given
To justify steps must use PROPERTIES
Solve. Justify your steps:
x - 2 = 11
Use 2-column proof to do this
x – 2 = 11
Given
Addition property of Equality (APOE)
x = 13
Simplify

5. x = -8 -12 = x – 4 -12 = x – 4 x – 4 = -12 +4 +4 Example 3 Given
To justify steps must use PROPERTIES
Solve. Justify your steps:
-12 = x – 4
Use 2-column proof to do this
-12 = x – 4
Given
x – 4 = -12
Symmetric (can SWITCH over = sign)
APOE
x = -8
Simplify

6. Example 4 Solve: -4x = -28 -4 -4 x = 7 Isolate the variable.
Opposite of Multiplication
is DIVISION.
x = 7

7. x = -8 -40 = 5x 5x = -40 5 5 Example 5 Given
To justify steps must use PROPERTIES
Solve. Justify your steps:
-40 = 5x
Use 2-column proof to do this
-40 = 5x
Given
5x = -40
Symmetric (can SWITCH over = sign)
Mult. Prop. of Equality (MPOE)
x = -8
Simplify

8. WELCOME Example 6 Solve: x = 7 3 (3) (3) x = 21 Isolate the variable.
Opposite of Division
is MULTIPLICATION.
Must do the same operation to BOTH sides of the equation to keep it balanced.
x = 21

9. 5 5 x = -15 Example 7 3 3 Given Solve. Justify your steps: 1 Simplify
Isolate the variable.
Multiply by the RECIPROCAL of the fraction. 5 3 5 3
Given 1
Mult. Prop. of Equality (MPOE)
Simplify
x = -15

10. Example 8 What do you know? W = width L = 3 times width 15 = length
Write and solve an equation for the following situation:
You are working on a banner for Friday’s pep rally. The length of the banner is 3 times the width. The length is 15 feet. What is the width?
What do you know?
W = width
L = 3 times width
15 = length
3w = 15
w = 5 feet

11. MUST SHOW ALL STEPS!! NO STEPS = NO CREDIT!!

12. Homework Section 3-1 Page 137 – 138
Solve & PROVE: 6 – 11, – 25, 36 – 39, 46 – 47 ;
Follow Directions: 30,

13. 3-2 Solve Two Step Equations
Objective: Students will create and solve equations in one variable.
Standards: A.REI.3 , A.CED.1 , A.REI.1

14. Example 1 +3 +3 x = 5 (4) (4) Solve: 4 x = 20 Isolate the variable.
Opposite of Subtraction
is ADDITION.
+3 +3
x = 5 4
(4)
(4)
Opposite of
Division
is MULTIPLICATION.
x = 20

15. y = 4 +12 +12 Example 2 20 = 8y - 12 Given 8y -12 = 20 8y = 32 8 8
To justify steps must use PROPERTIES
Solve. Justify your steps:
20 = 8y – 12
Use 2-column proof to do this
20 = 8y - 12
Given
8y -12 = 20
Symmetric (can SWITCH over = sign)
Add. Prop. of Equality (APOE)
8y = 32
Simplify
Mult. Prop. of Equality (MPOE)
y = 4
Simplify

16. Example 3 Solve and Prove: 5b – 7b = 4 -2b = 4 -2 -2 b = -2
Combine Like Terms FIRST!
SAME SIDE COMBINE!!!
5b – 7b = 4
Given
-2b = 4
Combine like terms
Isolate the Variable.
Opposite of Multiplication
is DIVISION.
Mult. Prop. Of
Equality (MPOE)
b = -2
Simplify

17. Example 4 x = 6 days 42x 42x = 252 -85 -85 42 42 + 85 = 337
To rent a booth at the county fairgrounds costs $42 per day plus a one time equipment fee of $85. Find the number of days Mr. Smith rented a booth if he paid a total of $337.
“per” means MULTIPLY. This is where your “x” goes!
STEP 1: Write the equation.
42x
+ 85 =
337
STEP 2: Solve the equation.
-85
-85
42x = 252 42 42
x = 6 days

18. Homework
Section 3-2 Page 144 – 145 SOLVE & PROVE: 6 – 20, Follow Directions: 22, 37, 38