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Variables and Equations Pre-Algebra

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Learning Objective I can solve equations with variables.

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Vocabulary Equation A mathematical sentence formed by placing an equal sign between two expressions. Example: x - 8 = 12 Solution A number that produces a true statement when substituted for the variable in an equation. Example: 2 + x = 5; x=3 is a solution

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Example 1 - Writing Verbal Sentences as Equations 1. The sum of x and 6 is 9. Equation: x + 6 = 9 2. The difference of 12 and y is 15. Equation: 12 - y = 15 3. The product of -4 and p is 32. Equation: -4p = 32 4. The quotient of n and 2 is 9. Equation: n/2 = 9

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Example 2: Checking Possible Solutions Tell whether 9 or 7 is a solution of x - 5=2. 1) Substitute 9 for x x - 5 = 2 9 - 5 = 2 ? 4 2 9 is not a solution

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Example 2: Checking Possible Solutions Tell whether 9 or 7 is a solution of x - 5=2. 1) Substitute 7 for x. x - 5 = 2 7 - 5 = 2 ? 2 = 2 7 is a solution

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Skill Check Write the verbal sentence as an equation. 1. The sum of 3 and z is -10. 3 + z = -10 2. The quotient of m and 6 is 4. m/6 = 6 Tell whether -5 or 5 is a solution of -8y=40. -5 is a solution

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Example 3 - Solving Equations Using Mental Math Equation: x + 3 = 11 Question: What number plus 3 equals 11? Solution: 8 Check: 8 + 3 = 11 Equation: 16 - m = 9 Question: 16 minus what number equals 9? Solution: 7 Check: 16 - 7 = 9

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Example 3 - Solving Equations Using Mental Math Equation: 20 = 5t Question: 20 equals 5 times what number? Solution: 4 Check: 20 = 5(4) Equation: y/6 = -3 Question: What number divided by 6 equals -3? Solution: -18 Check: -18/6 = -3

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Skill Check Solve the equations using mental math. 1. x - 10 = 7 x = 17 2. 2 + n = -6 x = -8 3. 3w = -15 x = -5 4. 4 = 36/x x = 9

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Skill Check Go-cart rides cost $5 each at a county fair. During the first day of the fair, the go-cart operator takes in a total of $1000. How many times did people ride the go-carts that day? Write and solve an equation to find the answer. 5x = 1000, x = 200; 200 times

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Classwork Assignment Page 87-88 #s 8-15, 20-31 even, 32-34

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