Download Section 1.1 Section 1.1 Guided Notebook Section 1.1 Linear

Section 1.1
Section 1.1 Guided Notebook
Section 1.1 Linear Equations in One Variable
Work through Section R.3 TTK on page 1.1-1
Work through Section R.3 TTK on page 1.1-1
Work through Section R.3 TTK on page 1.1-1
Work through Objective 1
Work through Objective 2
Work through Objective 3
Work through Objective 4
Section 1.1: Linear Equations in One Variable
Work through the You Try It Exercise: Evaluate Algebraic Expressions
showing all steps below.
Work through the You Try It Exercise: Simplify Algebraic Expressions
showing all steps below.
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Section 1.1
Work through the You Try It Exercise: Write Verbal Descriptions as
Algebraic Expressions showing all steps below.
Section 1.1 Objective 1: Determine if a Given Value Is a Solution to an Equation.
What is an equation?
What is an algebraic equation?
What do algebraic equations have that algebraic expressions do not have?
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Section 1.1
Work through the Interactive Video on page 1.1-3.
Which of the examples is NOT an equation? Why? Since it is not an
equation, what is it?
What is an equation in one variable? Write 3 examples.
Write the definition of Linear Equation in One Variable.
What is another name for linear equations? Why?
When are equations non-linear?
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Section 1.1
Work through the Interactive Video on 1.1-4.
Which of the equations is a linear equation? Why? Write the equation in
ax + b = c form.
What are solutions to an equation?
Work through the 3 problems in Example 1 showing all work below. For further
explanation watch the accompanying video.
Determine if the given value is a solution to the equation.
a. 2x + 3 = 11; x = 4
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b. 3y + 8 = 5y – 4; y = 2
c.
2
1 1
3
w− = ;w =
3
2 4
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Section 1.1
Section 1.1 Objective 2: Solve Linear Equations in One Variable
What are equivalent equations?
What is the simplest form that is the goal when solving a linear equation in one
variable?
What is used to find simpler equivalent equations?
What does the Caution Statement say on 1.1-7?
Watch the video on 1.1-7 explaining the properties of equality and answer the
questions below.
Addition Property of Equality
1. What does the Addition Property of Equality tell us?
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Section 1.1
2. Is this true for subtraction? Why or why not?
Multiplication Property of Equality
1. What does the Multiplication Property of Equality tell us?
2. Is this true for division? Why or why not?
3. What is the exception to this property?
Work through the 2 problems with Example 2 showing all work below.
Use the properties of equality to solve each equation.
a. 3x – 1 = 5
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b. 8 =
1
n+3
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Section 1.1
Work through Example 3 showing all work below. Be sure to show all work for
checking your solution.
Solve
6x – 5 = 2x - 3
If an equation contains non-simplified expressions what should you do first?
Work through Example 4 showing all work below. If you do not get the answer
shown in the link, watch the video for further explanation.
Solve
5(x – 6) – 2x = 3 – (x + 1)
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Section 1.1
Watch the video with the Note on 1.1-11 and answer the following questions.
1. In the first example 5(x – 4) = 10 which approach does the video consider
better?
2. What is recommended to do first as a general rule?
What is the best thing to do first if an equation contains fractions? How is that
accomplished?
Watch the video with Example 5 answering the following questions.
Solve
x 5 5
11
− = x−
3 12 6
12
1. What is the LCD?
2. What will multiplying by the LCD accomplish?
3. Write the equation after using the distributive property.
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Section 1.1
4. Why move the 4x term to the right?
5. Finish writing the steps to the solution of the equation.
Watch the video with Example 6 and answer the following questions.
Solve
1
x +1
(1 − x ) −
= −2
3
2
1. How do we know this equation is linear?
2. Why is 6 the LCD?
3. Rewrite the equation using the Distributive Property.
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Section 1.1
4. Show the remainder of the steps to solve the equation.
Is it necessary to clear the fractions first? Why or why not?
How can decimals be removed from an equation?
How can the appropriate power of 10 be determined?
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Section 1.1
Work through Example 7 showing all work below. For further explanation watch
the accompanying video.
Solve 0.5n – 0.25 + 0.075n = 0.5 – 0.025n
Watch the video with Example 8 answering the questions below.
Solve: 0.1(y – 2) + 0.03(y – 4) = 0.02(10)
1. How is the procedure for solving an equation with decimals similar to the
procedure for an equation with fractions?
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Section 1.1
2. How do you determine what to multiply both sides of the equation by
when the equation contains decimals?
3. What happens to the position of the decimal when you multiply by the
power of 10?
4. Show the remainder of the steps to solve the equation.
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Section 1.1
Write down the Guidelines for solving Linear Equation in One Variable.
Do you have to use every step?
Summarize the Caution statement on 1.1-16.
Section 1.1 Objective 3: Identify Equations That Are Contradictions and Those
That Are Identities.
What is a conditional equation?
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Section 1.1
What is a contradiction?
What is the solution set of an equation that is a contradiction?
How is this solution denoted?
What is an identity?
What is the solution set of an identity?
How is this solution denoted?
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Section 1.1
Work through Example 9 showing all steps below.
Use the properties of equality to determine if the equation is a contradiction
or an identity.
a. 5(x + 4) = 3(x + 7) + 2x
b. 3(x – 4) = x + 2(x – 6 )
In the final step the variables __________ out. A true statement indicates the
equation is a(n)_____________ and a false statement indicates the equation is
a(n) ________________.
Section 1.1 Objective 4: Use Linear Equations to Solve Application Problems.
What is the Problem Solving Strategy for Applications of Linear Equations?
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Section 1.1
Write down the 6 step process for Example 10. Show all work below.
Roger Staubach and Terry Bradshaw were both NFL quarterbacks. In 1973,
Staubach threw three touchdown passes more than twice the number of
touchdown passes thrown by Bradshaw. If the total number of touchdown
passes thrown between Staubach and Bradshaw was 33, then how many
touchdown passes did each player throw?
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Section 1.1
Watch the video with Example 11 answering the questions below
Before filling up her car, Kenya sees the price of gasoline as $3.26 per gallon.
When she finished filling the tank, Kenya owed $40.75. How many gallons of gas
did she purchase?
1. What is the given information?
2. What is the problem asking for?
3. What is the unknown?
4. How is the total cost of the gas obtained?
5. What is the equation?
6. Show the steps for solving the equation below.
7. Is the answer you obtained reasonable? Why or why not?
8. What is the answer to the question in the problem?
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Section 1.1
Watch the video with Example 12 answering the questions below.
A laptop computer is on sale for 15% off the original price. If the sale price is
$552.33, find the original price of the laptop.
1. What is the given information?
2. What is the problem asking for?
3. What is the variable and what does it represent?
4. How is the sale price related to the original price?
5. What is the original amount?
6. What is the discount amount?
7. What is the equation that represents this situation?
8. Show all steps to finish solving this equation.
9. What is the answer to the question in the problem?
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