1. Linear Equations and Inequalities
Unit 6
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2. Key Words
Inverse Operations
Inequality
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3. 6.1 Solving Equations by Using Inverse Operations
Focus: Model a problem with a linear equation, use an arrow diagram to solve the equation pictorially, and record the process symbolically.
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4. Equation A mathematical statement that two expressions are equal.
Example: 3n = 6
Remember: if you apply changes to one side of an equation, you must do the same to the other side!
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5. Inverse Operations
Inverse Operations “undo” or reverse each other’s results.
Addition and Subtraction are inverse operations.
So are Multiplication and Division.
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6. Example Solve: 3n = 6 Think: what is happening to the n?
The variable n is being multiplied by 3.
What would the inverse operation be?
The inverse of multiplying by 3 is dividing by 3!
So, divide both sides by 3 to solve the equation.
3𝑛 3 = 6 3 n = 2
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7. Recall: BEDMAS
How do we solve an equation when we have more than one operation?
Example: 𝑟 = 7.2
Inverse operations means we do the opposite operation. Our order of operations is BEDMAS, so the opposite of this is…
SAMDEB!
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8. Example: Use SAMDEB to solve 𝑟 4 + 3 = 7.2
𝑟 = 7.2
𝑟 = 7.2 – 3
𝑟 4 = 4.2
4 x 𝑟 4 = 4.2 x 4
𝑟 = 16.8
Subtraction/Addition
Multiplication/Division
Exponents
Brackets
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9. Example 1
Solve the equation: 12 = 2 𝑎 + 64
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10. Example 2
Solve the equation: 16 = 2(𝑥+5)
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11. Example 3
Solve: A number divided by 3, minus 13.5, is 2.8.
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12. Textbook Practice Questions
Pages 271 – 274
# 8, 10, 11abc, 13, 16, 18, 19, 20
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