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Chapter 2
Solving Linear
Equations
2.1 Writing Equations

4 Steps to Problem Solving
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Explore the problem (read the whole thing)
Plan the solution (write the equation)
Solve the problem
Check the solution (does it make sense?)

How to use a Formula
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Write the formula
Substitute for any known
variables
Solve the equation
Check the answer (does it
make sense?)
Perimeter=2l+2w
Area of a Square= lw
Area of a Triangle= ½ bh
Area of a Circle=  r2
2.2 Solving Equations by Using
Addition and Subtraction

To solve an equation means to find all values of the variable
that make it true

Addition Property of Equality:
– If you add the same amount to each side of the
equal sign, the equation is true
Ex: m – 48 = 29

Subtraction Property of Equality:
–
If you subtract the same amount from each side,
the equation is true
42 + d = 27
n + 5 = 40
2.3 Solving Equations by Using
Multiplication and Division

Multiplication Property of Equality:
–
If you multiply each side of the equal sign by the
same number, the equation is true
t/3 = 7
9/4g = 1/2
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Division Property of Equality:
–
If you divide each side of the equal sign by the
same number, the equation is true
13s = 195
-3x = 36
2.4 Solving Multi-Step Equations
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Add or Subtract the number farthest from the
variable
Multiply or divide the number next to the
variable
Simplify
Check your answer
Examples:
(p – 15)/9 = -6
2/3y – 25 = 115
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Even consecutive and odd consecutive
numbers = x, x+2, x+4, x+6….
Consecutive numbers = x, x+1, x+2, x+3…
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Find three consecutive integers whose sum is 21
Find three consecutive even integers whose sum
is -42
2.5 Solving Equations with
Variables on Each Side
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Distribute and/or combine like terms
Add or subtract the variables to one side
(move the smaller one)
Add or subtract the numbers to the other side
Solve as normal
Examples:
-2 + 10k = 8k -1
2m = 5 = 5(m – 7) -3m
2.6 Ratios and Proportions
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Ratio: a comparison of two numbers by division
–
x
x to y
x:y
y
ex: Your class has 21 students, 9 are boys and 12 are
girls
a. ratio of boys to girls ________________
b. ratio of students to boys _____________
Scale: a ratio that shows that a model is proportional to an
actual object
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Proportion: shows that two ratios are equal
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a and d are the extremes
b and c are the means
a c

b d
Solve a proportion by cross multiplying
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a
c
. 
b d
ad = bc
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Ex: Determine if it is a
proportion.
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Ex: Solve the proportion.
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a.
n 24

15 16
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b.
2  w 12

6
9
15 35

36 42
2.7 Percent of Change
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New # is greater than original # = % of increase
New # is less than original # = % of decrease
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To solve:
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new  original
#100  %
original
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Original: $25
New: $28
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Original: 16
New: 3
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Concert tickets cost
$45 each. The tax is
6.25%. What is the total
cost for one ticket?

A sweater is on sale for
35% off. The original
price is $38. What is
the sale price?
2.8 Solving for a Specific Variable

Use the normal order of operations and
problem solving steps to get the specific
variable on one side of the equal sign and
everything else on the other side of the equal
sign
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Solve 3x – 4y = 7 for y.
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Solve 2m – t = sm + 5
for m.
 Solve C=2 r for r
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Solve
s
1 2
at
2
for a.
2.9 Weighted Averages
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Weighted average: the sum of a product of
units and value per unit, divided by the sum
of the # of units
How many pounds of mixed nuts selling for $4.75
per pound should be mixed with 10 pounds of dried
fruit selling for $5.50 per pound, to obtain trail mix
that sells for $4.95 per pound?
# Units
Dried Fruit
10
Price per
Unit
5.50
Nuts
x
4.75
4.75x
Trail Mix
10 + x
4.95
4.95(10 + x)
550
55.0 + 4.75x = 4.95(10 + x)
SOLVE
FOR X
Product
An experiment calls for 30% solution of copper
sulfate. Kendra has 40ml of 25% solution. How
many ml of 60% solution should be added?
25% Solution
60% Solution
30% Solution
Amount/Units
40
x
40 + x
10 + .6x = .3(40 + x)
SOLVE
FOR X
Product
40 x .25= 10
.6x
.3(40 + x)