Presentation on theme: "To ‘undo’ a sequence of operations… … we perform the inverse operations in the reverse order. For example, compare the steps and operations to wrap a."— Presentation transcript:
To ‘undo’ a sequence of operations… … we perform the inverse operations in the reverse order. For example, compare the steps and operations to wrap a present with the steps and operations to unwrap the present: 1. Put present in box 2. Wrap box3. Put on ribbon 3. Take present out of box 2. Unwrap box 1. Take off ribbon
Inverse Operations… … ‘undo’ or reverse each other’s results. In order to be able to solve equations, you MUST know the mathematical inverse operations:
We can use inverse operations to solve equations… … to do this, we determine the operations that were applied to the variable to build the equation. We then use INVERSE OPERATIONS to isolate the variable by ‘undoing’ these operations.
Here’s an example… x + 5 x + 5 x = 8 13 Your job is to figure out the value of ‘x’. In this example, finding ‘x’ is easy, but we need a strategy to determine ‘x’ when the questions get harder! What is the inverse operation? What mathematical operations have been applied to the variable to build this equation? - 5 BUILD SOLVE
Let’s look at a few more examples: xx – 3 x = 12 9 t7t t = 3 21 What does the ‘math’ look like when we solve these equations? BUILD SOLVE
How can you check to see if you are correct? d x 4.5 4.5d - 3.2 4.5d – 3.2 + 3.2÷ 4.5 Let’s try a harder one… d = -3.4-15.3-18.5 Inverse Operations! BUILD SOLVE
Here’s a few more… Make sure you ‘build’ the equation first and then use the inverse to solve! Have you noticed a connection between solving equations and BEDMAS?
Here’s the hardest one yet! x +1 x + 1 x 7 7(x + 1) ÷2 x 2÷ 7 - 1 The KEY thing to remember about solving any equation is: Whatever you do to one side of an equation, you must do to the other side to keep the equation balanced! x = 3 428 14
How about a ‘word problem’? How about a ‘word problem’? A rectangle has length 3.7 cm and perimeter 13.2 cm. Write an equation that can be used to determine the width of the rectangle. Write an equation that can be used to determine the width of the rectangle. Solve the equation. Solve the equation. Verify (check) your solution. Verify (check) your solution.
Working with %... Seven percent of a number is 56.7. Write, then solve an equation to determine the number. Write, then solve an equation to determine the number. Check the solution. Check the solution. What does OF mean in math? Choose the method that works best for you, but you MUST show an equation!
Page 271: 5ab, 6ac, 7 (discuss), 8be, 9ab, 10bcf, 11ad, 12 (discuss), 13abc, 14abc, 16ab, 17ab, 18acd (be prepared to go over in class!)
What are the rules for solving equations? Build the equation (either on paper) or in your mind. Whatever operation you do to one side, you MUST do to the other side in order to keep the equation balanced! ALWAYS CHECK YOUR WORK!