�Solving Two Step Equations

March 2023 Algebra Unit

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Aligns with:

McGraw-Hill 5.3,

Kaplan 2015 p. 350-351,

GED EssentialEd: http://www.math.com/school/subject2/practice/S2U3L6/S2U3L6Pract.html

iPathways Unit Variables and Algebraic Expressions, Lesson Solving Algebraic Equations Using the Multiplication and Addition Principal,

Khan Academy (https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-variables-expressions/cc-7th-2-step-equations-intro/e/linear_equations_2)

Two-Step Equations

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• Warm up
• Review
• Looking ahead
• One-Step vs Two-Step Equations
• Practice
• Exit

Warm up

Find all the factors of each of these numbers:

Warm Up: PEMDAS, aka Order of Operations

Simplify the following expressions:

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1. 8 + 16 ÷ 2 = __________ 2. 10 x (10 - 3) = __________

3. 7 x 3 – (3 + 8) = __________ 4. 24 ÷ (16 – 4 x 2) = __________

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PEMDAS Review (if needed)

What is PEMDAS?

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• Aka Order of Operations: what you do first, next, etc.

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• Operations include (), exponents or roots, *, /, +, -
• ()
• then exponents or roots
• then * or /
• then + or -

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Warm Up: One-Step Equations

• Solve the following equations:

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5y = 35 x + 4 = -9

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n-1 = 10 7 = b-12

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z/3 = 2 ½ (x) = 8

Review Solving 1-step Equations (if needed)

To solve 1-step equations:

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• Identify the variable
• Identify the operation being performed on the variable
• Reverse the operation performed on the variable, on both sides of the equation
• You are left with the solution

Example: -5x = 25

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• The variable is x
• It is being multiplied by -5
• Reverse of multiply is divide, so divide both sides by -5
• The -5 cancels out on the left side
• On the right side, 25/-5 = -5
• So, x = -5
• DON’T FORGET TO CHECK YOUR SOLUTION BY PLUGGING IT BACK IN

Looking Ahead: Two-Step Equations

Solve the following equations:

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1. 5x + 1 = 41

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• -2k + 3 = 1

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• y/6 – 12 = -10

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• (-1/8)z + 6 = 14

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Isolating the Variable when Solving Equations

We need to isolate the variable, but there are two or more operations in the equation. What order do we use to isolate a variable?

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• Use distributive property and combine like terms if needed. Example: 2(4x+3) – 5 becomes …

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• Then think about unpeeling around the variable, taking the “loose” or outer layers first.

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• Your goal is to leave the variable all by itself on one side of the equation.

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Isolating the Variable when Solving Equations

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Examples: what operations do we need to “undo” to isolate the variable, in the examples below?

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2x + 4 9 - b

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x/3 + 5 6k - (5 + 3)

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8 - 7b 4 + (3y - 2 )

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6x + 5 – 2x = 25 -4(x-6) = 2x

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Creating 2-step equations from 1-step equations (if needed)

Solving Equations 2-Step Template:�Recording the Steps

DON’T FORGET TO CHECK YOUR SOLUTION BY PLUGGING IT BACK IN

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Solve: 3x + 6 = 12

3x + 6 = 12

- 6 -6

3x = 6

/3 /3

X = 2

Solve: -x + 5 = -20

-x + 5 = -20

- 5 -5

-x = -25

/-1 /-1

X = 25

+ 8 + 8

·6 ·6

X = -144

- 5 - 5

·(-10) ·(-10)

X = 120

- 4 - 4

X = 32

- 33 - 33

X = - 15

Exit Practice! �Take out a sheet of paper. Copy and Solve the following questions.

1)

2)

3)

4)

10 = 6 x + 34

Exit Practice Answers �

1)

2)

3)

4)

10 = 6 x + 34 X=-4

Word Problem (2-Step) Practice

• Dave has 500 baseball cards. This is as many as Eric and Travis have, combined.
• What do you know, so far??
• Are there any relationships or operations you can show?

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• Eric has three times as many cards as Travis has.
• What info does this give you??

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• Using x to represent the number of cards Travis has, how many cards does Eric have?
• If you are lost, start with the unknowns, and work your way up from there.

Word Problem (1-Step) Practice

• There are twice as many women as men in a class on auto repair.
• What do you know so far??
• Are there any relationships or operations you can show?

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• If there are 24 students total in the class, how many are women?
• What does this tell you?
• What is your unknown?

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Word Problem (2-Step) Practice

• The sum of three consecutive numbers is 105.
• What does this tell you?
• Can you identify the unknowns?
• Are there any relationships or operations among the unknowns?

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• What is the greatest of the three numbers?