VHS A1 1.1 Variables

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Variables and expressions for Algebra 1A

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Lessons from the Math Zone: Variables Click to Start Lesson

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Lessons from the Math Zone Variables © Copyright 2006, Don Link Permission Granted for Educational Use Only

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Variables Vary x = 5 7 6 8 9 10 10 15 20 25 30 40 50 100 200 300 1,000 2,000 3,000 4,000 5,000 1.0 1.1 1.2 1.3 1.4 1.5 2.5 3.5 4.5 5.5 5.5 0.01 0.02 3.33 –1 –2 –3 –4 –5 –1.5 –2.6 –3.7 –4.8 –5.9 –6.0

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Algebraic Expressions An Algebraic Expression is an expression that contains at least one Variable. x + 14 3x + 1 9 – x

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9 – Using Variables x = + 14 3 + 1 =22 =25 x x =1 x =2 x One way to use variables is to substitute their numerical value into an algebraic expression. (8) (8) (8) (8) 8

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9 – One way to use variables is to substitute their numerical value into an algebraic expression Using Variables x = 8 + 14 3 + 1 =22 =25 x x =1 x =2 x Way to Go!

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Let’s Practice x – 3 = 1 x = 4 2x – 3 = 5 9x + 3 = 39 10 – 2x = 2 x + x = 8 x ÷ 2 = 2 2(x + 5) = 18 (x +10)×(x – 2) = 28 3x + 4x – 2 = 26 5x = 20

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Let’s Practice x – 3 = 1 x = 4 2x – 3 = 5 9x + 3 = 39 10 – 2x = 2 x + x = 8 x ÷ 2 = 2 2(x + 5) = 18 (x +10)×(x – 2) = 28 3x + 4x – 2 = 26 5x = 20 High Five!

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Let’s Practice with Two Variables a+b–2 = 6 a = 3 2b – 3a = 1 5a ÷ b = 3 ab = 15 a(b + 5) = 30 (a +10)×(b – 2) = 39 3ab + 4a – 2 = 55 5a–b = 10 b = 5

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Let’s Practice with Two Variables a+b–2 = 6 a = 3 2b – 3a = 1 5a ÷ b = 3 ab = 15 a(b + 5) = 30 (a +10)×(b – 2) = 39 3ab + 4a – 2 = 55 5a–b = 10 b = 5 Good Job!

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Another way to use a variable is as an unknown value in an algebraic equation. Unknown Variables 5 + x = 8 An Equation Claims that the Left Side = the Right Side Unknown Left Side Right Side

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Unknown Variables 5 + x = 8 An Equation If: Left Side Right Side, = then the “equation is .” true If: Left Side Right Side, ≠ then the “equation is .” false To find the unknown value that makes the equation true, we “solve the equation for x.”

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5 + = 8 If x = 7 , the equation is 7 Unknown Variables True? False? True? False? x 12 8 3 If x = 3 , the equation is = 8

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Solving an Equation Solving an equation means finding a value for the unknown that makes the equation true. 5 + x = 8 What value for x will make this equation true? 3 is a solution to the equation.

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Let’s Practice Using Different Variables x – 3 = 10 4w – 3 = 5 2δ ÷ 3 = 6 20 – □ = 2 5a = 20 x = 13 a = 4 w = 2 δ = 9 □ = 18

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Let’s Practice Using Different Variables x – 3 = 10 4w – 3 = 5 2δ ÷ 3 = 6 20 – □ = 2 5a = 20 x = 13 a = 4 w = 2 δ = 9 □ = 18 Cookin’!

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x + 17 = 25 8 x = 8 x – 3 = 4 Variables: Summary and Review 1 Substitute the numerical value of a variable into an algebraic expression 2 “Solve the equation for x.” x = 4 1

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