2To ‘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 box2. Wrap box3. Put on ribbon3. Take present out of box2. Unwrap box1. Take off ribbon
3Inverse Operations… SUBTRACTION Addition & MULTiPLICATION & Division … ‘undo’ or reverse each other’s results.In order to be able to solve equations, you MUST know the mathematical inverse operations:SUBTRACTIONAddition &MULTiPLICATION &Division
4We 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.
5What is the inverse operation? Here’s an example…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 mathematical operations have been applied to the variable to build this equation?+ 5BUILDxx + 5SOLVE13x = 8What is the inverse operation?- 5
6Let’s look at a few more examples: BUILDxx – 3t7tSOLVE921x = 12t = 3What does the ‘math’ look like when we solve these equations?
7How can you check to see if you are correct? Let’s try a harder one…x 4.5- 3.2BUILDd4.5d4.5d – 3.2SOLVEd = -3.4-15.3-18.5How can you check to see if you are correct?÷ 4.5+ 3.2Inverse Operations!
8Have you noticed a connection between solving equations and BEDMAS? 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?
9Here’s the hardest one yet! +1x 7÷2xx + 17(x + 1)x = 342814- 1÷ 7x 2The 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!
10How 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.Solve the equation.Verify (check) your solution.
11What does OF mean in math? Working with %...Seven percent of a number is 56.7.Write, then solve an equation to determine the number.Check the solution.Choose the method that works best for you, but you MUST show an equation!What does OF mean in math?
12Assignment Time!Page 271: 5ab, 6ac, 7 (discuss), 8be, 9ab, 10bcf, 11ad, 12 (discuss), 13abc, 14abc, 16ab, 17ab, 18acd (be prepared to go over in class!)
13What 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!