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 box 3. 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 13 What mathematical operations have been applied to the variable to build this equation? +5 BUILD What is the inverse operation? SOLVE -5 Let’s look at a few more examples: 3 x 9 7t 21 BUILD SOLVE What does the ‘math’ look like when we solve these equations? Let’s try a harder one… 4 .5 d 3 .2 1 8 .5 x 4.5 - 3.2 BUILD SOLVE ÷ 4.5 Inverse Operations! + 3.2 How can you check to see if you are correct? Here’s a few more… Make sure you ‘build’ the equation first and then use the inverse to solve! m 1.5 4 r 4 3 7.2 Have you noticed a connection between solving equations and BEDMAS? Here’s the hardest one yet! +1 x7 ÷2 ( 2 ) 7 ( x 1) 7 ( x 1) 2 -1 ÷7 x2 14 ( 2 ) 2 7 ( x 1) 28 7 7 ( x 1 1) 4 1 x 3 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! 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. Solve the equation. Verify (check) your solution. Working with %... Seven percent of a number is 56.7. Write, then solve an equation to determine the number. 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!

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# 6.1 Solving Equations by Using Inverse Operations