Download Solving Multi-Step Equations - peacock

Solving Multi-Step Equations
Section 2-3 Part 2
Goals
Goal
• To solve multi-step
equations in one variable.
Rubric
Level 1 – Know the goals.
Level 2 – Fully understand the
goals.
Level 3 – Use the goals to
solve simple problems.
Level 4 – Use the goals to
solve more advanced problems.
Level 5 – Adapts and applies
the goals to different and more
complex problems.
Vocabulary
• None
Two Special Techniques
Two Special Techniques for Solving Multi-Step
Equations.
1. Clear the equation of fractions by multiplying both
sides of the equation by the LCD of all denominators
in the equation.
2. Simplify equations with decimal coefficients by
multiplying both sides of the equation by a factor 10
(usually 10 or 100) to make all the coefficients whole
numbers.
Example: Clear Fractions
Using the LCD
Solve
.
Multiply by the LCD to clear the fractions.
Multiply both sides by 24, the
LCD of the fractions.
Distribute 24 on the left side.
3y – 18 = 14
+18 +18
3y = 32
Simplify.
Since 18 is subtracted from 3y, add
18 to both sides to undo the
subtraction.
Example: Continued
3y = 32
3y = 32
3
3
Since y is multiplied by 3, divide
both sides by 3 to undo the
multiplication.
Example: Clear Fractions
Using the LCD
Solve:
1
1
3
m 

5
2
4
10
1
1
 20  m   20  
5
2
4
M (20)
Simplify
A(10)
D(4)
5
3
 20 
4
4m  10  15
4m  25
m
25
4
Your Turn:
Solve
.
Multiply by the LCD to clear the fractions.
Multiply both sides by 12, the LCD
of the fractions.
Distribute 12 on the left side.
8r + 9 = 7
–9 –9
8r = –2
Simplify. Since 9 is added to 8r,
subtract 9 from both sides to
undo the addition.
Your Turn: Continued
8r = –2
8r = –2
8
8
Since r is multiplied by 8, divide
both sides by 8 to undo the
multiplication.
Your Turn:
1.
1 1
1
  x
2 3
5
21
x
10
2.
2
5 5
x 
3
6 4
5
x
8
Your Turn:
3.
3x x
 5
4 8
x 8
4.
n 3n 1
 
5 10 5
n  2
Example: Simplifying
Decimal Coefficients
Solve 1.5 = 1.2y – 5.7.
Multiply by a factor of 10 to clear the decimals.
(10)1.5 = (10)1.2y – (10)5.7
Multiply both sides by 10, to make
the decimals whole numbers.
15 = 12y – 57
+ 57
72 = 12y
72 = 12y
12
12
6=y
+ 57
First y is multiplied by 12. Then 57 is
subtracted. Work backward: Add 57
to both sides.
Since y is multiplied by 12, divide both
sides by 12 to undo the
multiplication.
Example: Simplifying
Decimal Coefficients
Solve:
M (100)
A(20)
D(40)
0.4x  0.2  0.16
40x  20  16
40x  4
x  0.1
01
40 4 0
40
.
Your Turn:
Solve:
M (1000)
A(20)
D(2)
0.002k  0.02  4.02
2k  20  4020
2k  4000
k  2000
Your Turn:
1. 2.5n  0.1n  9.8
n  28
2. 0.25  d  12   4
d  28
Joke Time
• What is a forum?
• Two-um plus two-um!
• Why did Mickey Mouse go to space?
• To visit Pluto.
•
•
•
•
Knock Knock? Who’s There?
Armageddon!
Armageddon who?
Armageddon out of this place!
Assignment
• 2.3 Pt 2 Exercises Pg. 107 – 108: #8 – 36
even