Linear Equations and Inequalities Unit 6 Math-9-6-1

Key Words Inverse Operations Inequality Math-9-6-1

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. Math-9-6-1

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! Math-9-6-1

Inverse Operations Inverse Operations “undo” or reverse each other’s results. Addition and Subtraction are inverse operations. So are Multiplication and Division. Math-9-6-1

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 Math-9-6-1

Recall: BEDMAS How do we solve an equation when we have more than one operation? Example: 𝑟 4 + 3 = 7.2 Inverse operations means we do the opposite operation. Our order of operations is BEDMAS, so the opposite of this is… SAMDEB! Math-9-6-1

Example: Use SAMDEB to solve 𝑟 4 + 3 = 7.2 𝑟 4 + 3 = 7.2 𝑟 4 + 3 - 3 = 7.2 – 3 𝑟 4 = 4.2 4 x 𝑟 4 = 4.2 x 4 𝑟 = 16.8 Subtraction/Addition Multiplication/Division Exponents Brackets Math-9-6-1

Example 1 Solve the equation: 12 = 2 𝑎 + 64 Math-9-6-1

Example 2 Solve the equation: 16 = 2(𝑥+5) Math-9-6-1

Example 3 Solve: A number divided by 3, minus 13.5, is 2.8. Math-9-6-1

Textbook Practice Questions Pages 271 – 274 # 8, 10, 11abc, 13, 16, 18, 19, 20 Math-9-6-1