Download Example 1 - Cloudfront.net

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
Vocabulary
Inverse Operations:
Two operations that undo each other.
Examples:
Addition & Subtraction
Multiplication & Division
Equivalent Equations:
Equations that have the same
solution(s).
Example 1
Solve:
Isolate the variable.
x by itself by doing
x + 9 = 3 Get
the opposite operation.
-9 -9 What you do to ONE
SIDE, you must do to
x = -6 the OTHER SIDE of
the equation to keep it
balanced.
Example 2
To justify steps
Solve. Justify your steps: must use
PROPERTIES
x - 2 = 11
Use 2-column
proof to do this
x – 2 = 11 Given
+2 +2
x = 13
Addition property of Equality
(APOE)
Simplify
Example 3
To justify steps
Solve. Justify your steps: must use
PROPERTIES
-12 = x – 4
Use 2-column
proof to do this
-12 = x – 4 Given
x – 4 = -12
+4 +4
x = -8
Symmetric (can SWITCH over = sign)
APOE
Simplify
Example 4
Solve:
Isolate the variable.
of Multiplication
-4x = -28 Opposite
is DIVISION.
-4 -4
x=7
Example 5
To justify steps
Solve. Justify your steps: must use
PROPERTIES
-40 = 5x
Use 2-column
proof to do this
-40 = 5x Given
5x = -40
5
5
x = -8
Symmetric (can SWITCH over = sign)
Mult. Prop. of Equality (MPOE)
Simplify
Example 6
Solve:
Isolate the variable.
of Division
(3) x = 7(3) Opposite
is MULTIPLICATION.
3
Must do the same
operation to BOTH
x = 21
sides of the equation to
keep it balanced.
Example 7
Solve. Justify your steps:
3
Isolate the variable.
x  9
Multiply by the
5
RECIPROCAL of the
5 3 x  9 5 Given
fraction.
3 5
1 3 Mult. Prop. of Equality (MPOE)
 45
x
3
Simplify
x = -15
Example 8
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?
W = width
15 = length
3w = 15
3
3
w = 5 feet
What do you know?
L = 3 times width
MUST SHOW ALL STEPS!!
NO STEPS = NO CREDIT!!
Homework
Section 3-1
Page 137 – 138
Solve & PROVE: 6 – 11,
20 – 25, 36 – 39, 46 – 47 ;
Follow Directions: 30, 53 - 56
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
Example 1
Solve:
x
3  2
4
+3 +3
(4) x
= 5(4)
4
x = 20
Isolate the variable.
Opposite of
Subtraction
is ADDITION.
Opposite of
Division
is
MULTIPLICATION.
Example 2
To justify steps
Solve. Justify your steps: must use
PROPERTIES
20 = 8y – 12
Use 2-column
20 = 8y - 12 Given
proof to do this
8y -12 = 20
Symmetric (can SWITCH over = sign)
+12 +12 Add. Prop. of Equality (APOE)
8y = 32 Simplify
8 8 Mult. Prop. of Equality (MPOE)
y =4
Simplify
Example 3
Solve and Prove:
5b – 7b = 4
5b – 7b = 4
-2b = 4
-2
-2
b = -2
Given
Combine Like
Terms FIRST!
SAME SIDE
COMBINE!!!
Combine like terms
Isolate the
Mult. Prop. Of
Equality (MPOE) Variable.
Opposite of
Simplify
Multiplication
is DIVISION.
Example 4
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
Homework
Section 3-2
Page 144 – 145
SOLVE & PROVE: 6 – 20,
28 - 30
Follow Directions: 22, 37, 38