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Definition: Inverse Operations - Are opposite operations. Adding is the inverse of subtracting and subtracting is the inverse of adding. • The goal when solving equations is to isolate the variable. • We isolate the variable by completing inverse operation(s). • Remember, what you do to one side of the equation you MUST do to the other! Inverse Actions and Operations What is the inverse of putting items in a box? What is the inverse of tying your shoes? What is the inverse of doing your homework? What is the inverse of multiplication? Example 1 x + 62 = 93 x + 62 = 93 - 62 - 62 x = 31 Check: Example 2 81 = 17 + y Original equation Subtract 62 from BOTH sides to isolate x. Solution Check your work to see if your answer is correct! x + 62 = 93 Does 31 + 62 = 93? 93 = 93 Yes, it does 81 = 17 + y - 17 – 17___ 64 = y or y = 64 Original equation Subtract 17 from BOTH sides to isolate y. Solution Check: 81 = 17 + y Does 81 = 17 + 64? 81 = 81 Yes, it does Check your work to see if your answer is correct! Example 1 p–2=5 p–2=5 +2 +2 p=7 Example 2 40 = x - 11 Original equation Add 2 to BOTH sides to isolate p. Solution Check: p-2=5 Does 7 - 2 = 5? 5=5 Yes, it does Check your work to see if your answer is correct! 40 = x – 11 + 11 + 11 51 = x or x = 51 Original equation Add 11 to BOTH sides to isolate x. Solution Check: 40 = x - 11 Does 40 = 51 – 11? 40 = 40 Yes, it does Check your work to see if your answer is correct! Try these: Show all work and check your solutions. 1.) x + 16 = 90 2.) 21 = a + 13 3.) a - 33 = 49 4.) 45 = d - 11 Real-Life Application Some surfers recommend that the length of a beginner’s surfboard be 14 inches greater than the surfer’s height. If a surfboard is 82 inches, how tall should the surfer be to ride it? Set up and solve an equation to find the answer. Real-Life Application When Theodore Roosevelt became president of the United States, he was 42 years old. He was 27 years younger than Ronald Reagan when Reagan became president. How old was Reagan when he became president? Set up and solve an equation to find the answer.