Solving Linear Equations

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Solving Linear Equations
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• Chapter 3 is about solving linear equations. In
  this chapter you will learn
• techniques for solving linear equations
  systematically
• ways to apply ratios, rates, percents, and
  problem solving strategies.

3.1
Solving Equations Using Addition and Subtraction
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Write the original equation
Add 9 to Each Side
Simplify
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Write the original equation
Simplify
Subtract 2 from each side
Simplify
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Linear Equation Variable is raised to the first
power and does not occur in a denominator, inside
a square root symbol, or inside absolute value
symbols.
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Solving Linear equations using real life
situations
You have x dollars and your friends pays you back
the 7 dollars he owes you. You know have 9
dollars. How much did you have before he paid
you?
Subtract 7 from each side
Simplify
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Solving Equations Using Multiplication and
Division
3.2
You can solve linear equations by using
multiplication and division.
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A time lapse camera photographed a growing plant
at the rate of 25 frames per hour over several
days. For how many days was the plan
photographed if there were a total of 17,400
frames.
Write the problem
Simplify
Transform (Divide)
Simplify
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Ratio of a to b a/b Two triangles if they
have equal corresponding angles are similar.
d
a
10
5
6
y
b
f
c
e
x
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The ratio of abc is equal to the ratio of def
What is x and y ?
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Solving Multi-Step Equations
3.3
Using Two or More Transformations
Solving a linear equation may require two or more
transformations. Here are two guidelines.

• Simplify one or both sides of the equation (If
  needed)

• Use inverse operations to isolate the variable

Solving a linear equation
Solve
Write the equation
Subtract 6 from each side
Simplify
Multiply each side by 3
Simplify
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Combining Like Terms First
Solve
Write the equation
Combine Like Terms
Add 8 to both Sides
Simplify
Divide each side by 4
Simplify
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Using the Distributive Property
Solve
Do all Steps ..or
Do some steps mentally
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Distributing a negative
Solve
Write the equation
Use the Distributive Property
Combine Like Terms
Subtract 6 from both sides
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Multiplying by a Reciprocal First
Solve
Write the equation
Multiply by the Reciprocal
Simplify
Subtract 3 from both sides
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Solving Real-Life Problems
Using a Known Formula
A body temperature of 95 ?F or lower may indicate
the medical condition called hypothermia. What
temperature in the Celsius scale may indicate
hypothermia?
The Fahrenheit and Celsius scales are related by
the equation F9/5C 32
Write the equation
Substitute for F
Subtract 32 from both sides
Multiply by the reciprocal
Reduce
Simplify
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Using a verbal model
The speed of a falling object increases 32 ft/sec
for each second it falls. How many seconds will
it take the speed of a rock dropped from a very
high cliff to increase from 50 ft/sec to 210
ft/sec?
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Solving Equations with Variables on Both Sides
3.4
Collecting Variables on one side
Some equations have variables on both sides. To
solve such equations, you may first collect the
variable terms on the side with the greater
variable coefficient.
Collect variables on Left Side
Solve
Collect variables on Right Side
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Many solutions or No Solution
The answer is any number (Many solutions).
Since -9 is not -10 there is NO Solution
Solving more complicated equations
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Solving Real-Life Problems
Using a verbal Model
A video store charges 8 to rent a video game for
five days. You must be a member to rent from the
store, but the membership is free. A video game
club in town charges on 3 to rent a game for
five days, but membership in the club is 50 per
year. Which rental plan is more economical?
What does this mean?
With plan one it is cheap until you rent 10
videos and then the second plan is better.
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Linear Equations and Problem Solving
3.5
Drawing a Diagram
You have used a verbal model to solve real-life
problems. Verbal models can be used with other
problem solving strategies, such as drawing a
diagram.
Visualize a Problem
A page of your school yearbook is 8 ½ inches by
11 inches. The left margin is ¾ inch and the
space to the right of the pictures is 2 7/8
inches. The space between pictures is 3/16 inch.
How wide can each picture be to fit three across
the width of the page?
Write and equation to solve the problem.
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Solving Decimal Equations
3.6
Solving Decimal Equations
Exact solutions are not always practical and you
must use rounded solutions. Rounded solutions
can lead round-error, as you will see in the next
example.
Rounding for a Practical Answer
Three people wan tot share equally in the cost of
a pizza. The pizza costs 12.89. You can find
each persons share by solving 3x12.89.
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Rounding for the final answer
Equations Involving Decimals
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Formulas and Functions
3.7
Solving Formulas
In this lesson you will work with equations that
have more than one variable. A formula is an
algebraic equation that relates two or more
real-life quantities.
Solving and Using an Area formula

• Use the formula for the area of a rectangle,
  Alw
• Find a formula for l in terms of A and w.
• Use the new formula to find the length of a
  rectangle that has an area of 35 square feet and
  a width of 7 feet.

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Rewriting Equations in Function Form
Rewriting Equations in Function Form