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Solving Equations Using Addition and Subtraction Objectives: • A.4f Apply these skills to solve practical problems. • A.4b Justify steps used in solving equations. • Use a graphing calculator to check your solutions. To Solve an Equation means... • To isolate the variable having a coefficient of 1 on one side of the equation. • Ex: x = 5 is solved for x. • y = 2x - 1 is solved for y. Addition Property of Equality For any numbers a, b, and c, if a = b, then a + c = b + c. What it means: You can add any number to BOTH sides of an equation and the equation will still hold true. An easy example: • Would you ever We all know that 7 = 7. leave the house with only one shoe on? Does 7 + 4 = 7? NO! • Would you ever put blush on just one But 7 + 4 = 7 + 4. cheek? The equation is still • Would you ever true if we add 4 shave just one side of your face? to both sides. Let’s try another example! x - 6 = 10 Add 6 to each side. x - 6 = 10 +6 +6 x = 16 • Always check your solution!! • The original problem is x - 6 = 10. • Using the solution x=16, Does 16 - 6 = 10? • YES! 10 = 10 and our solution is correct. What if we see y + (-4) = 9? Recall that y + (-4) = 9 • Check your solution! is the same as y - 4 = 9. • Does 13 4 = 9? Now we can use the • YES! 9=9 and addition property. our solution is y-4=9 correct. +4 +4 y = 13 How about -16 + z = 7? • Remember to always • Check you solution! use the sign in front of the number. • Does -16 + 23 = 7? • Because 16 is negative, we need to add 16 to both sides. • YES! 7 = 7 and our solution is correct. • -16 + z = 7 +16 +16 z = 23 A trick question... -n - 10 = 5 +10 +10 -n = 15 • Do we want -n? NO, we want positive n. • If the opposite of n is positive 15, then n must be negative 15. • Solution: n = -15 • Check your solution! • Does -(-15)-10=5? • Remember, two negatives = a positive • 15 - 10 = 5 so our solution is correct. Subtraction Property of Equality • For any numbers a, b, and c, if a = b, then a - c = b - c. What it means: • You can subtract any number from BOTH sides of an equation and the equation will still hold true. 3 Examples: 1) x + 3 = 17 -3 -3 x = 14 • Does 14 + 3 = 17? 2) 13 + y = 20 -13 -13 y=7 • Does 13 + 7 = 20? 3) z - (-5) = -13 • Change this equation. z + 5 = -13 -5 -5 z = -18 • Does -18 -(-5) = -13? • -18 + 5 = -13 • -13 = -13 YES! Try these on your own... x + 4 = -10 x – 14 = -5 y – (-9) = 4 3 – y= 7 12 + z = 15 -5 + z = -7 The answers... x = -14 x=9 y = -5 y = -4 z=3 z = -2