1. Equations

2. Objective: solve linear equations with a variable on one side.

3. 4a = 24 This means “4 multiplied by a” What is the inverse operation? Division a = 24 4 = 6

4. b = 3 5 This means “b divided by 5” What is the inverse operation? Multiplication b = 3 x 5 = 15

5. Simple Equations (1 step) Includes variable, one operation, and answer Includes variable, one operation, and answer X – 2 = 8 X – 2 = 8 4 + X = 8 4 + X = 8 6/x = 3 6/x = 3 2x = 10 2x = 10 Keep the equation balanced! Use INVERSE OPERATIONS to solve.

6. Tara and Tom were solving linear equations. To find the value of x in a linear equation, Tara asked herself, “What number, when you subtract four from it, is equal to twelve?” Tom solved a linear equation by adding four to both sides. It is possible that the two students were solving the same equation? How do you know?

7. Medium 3a + 8 = 35 Let’s make this question into a low simple question. We know how to solve those! This is the only bit that is different. We can use inverse operations to get rid of it. This says “add 8” What is the inverse operation? Subtract 3a = 35 - 8 3a = 27 Look! A simple question! a = 27 3 = 9

8. Equations (2 step) Includes variable, two operations, and answer Includes variable, two operations, and answer 3X – 2 = 8 3X – 2 = 8 4 + 5X = 19 4 + 5X = 19 6/x + 4 = 7 6/x + 4 = 7 2x - 6 = 10 2x - 6 = 10 Keep the equation balanced! Use INVERSE OPERATIONS to solve. Work Backwards.

9. Sal explained how he solved a linear equation by saying, “I undid the addition by subtracting from both sides. Then I undid the multiplication by dividing both sides. That told me the value of x was ten.” What equation might Sal have solved?

10. The hand shown is covering a term in a linear equation. What might the hidden term be and what as a result, would be the value of x? 4 + ø = 16

11. Take it up a level! Objective: solve linear equations with an unknown (variable) both sides.

12. Level 2 5a + 3 = 2a + 12 Let’s start by removing this. This says add 3 What is the inverse operation? Subtract 3 Doing this removes the add 3, but remember to subtract 3 from the other side too! 5a = 2a + 12 - 3 5a = 2a + 9 Now, let’s remove this. To “get rid of” our 2a, we have to subtract 2a 5a – 2a = 9 3a = 9 a = 9 A 3 = 3

13. Equations (variables on both sides) Includes variable in several places, more than one operation, and answer Includes variable in several places, more than one operation, and answer 7x + 10 = 2x 7x + 10 = 2x 11x = 24 + 8x 11x = 24 + 8x 8y – 3 = 6y +17 8y – 3 = 6y +17 7k + 12 = 8 – 9k 7k + 12 = 8 – 9k Keep the equation balanced! Use INVERSE OPERATIONS to solve. Start by getting the variable on one side!