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Transcript
Two-Step Equations B Tool Box: 1. 2. 3. Summary: Inverse Operations Properties of Equality Like Terms Question: Two-Step Equations contain “two” operations To solve two-step equations, use inverse operations to “undo” each operation in reverse order EXAMPLE: 𝟓𝒙 − 𝟐 = 𝟏𝟑 𝟓𝒙 − 𝟐 = 𝟏𝟑 1.Write the equation 2. Draw railroad tracks 3. Isolate the variable 4. Addition Property of Equality (add 2 to both sides of the equation) 𝟓𝒙 − 𝟐 = 𝟏𝟑 𝟓𝒙 − 𝟐 = 13 +2 + 2 𝟓𝒙 = 𝟏𝟓 5𝑥 = 5 𝟖 = 𝟖 = -15 -7 = ( - 3) -7 = 21 15 𝟖 = EXAMPLE: 𝒄 + −𝟑 𝒄 + - −𝟑 5. Simplify/Combine Like Terms 6. Division Property of Equality (Divide both sides of the equation by 5) 7. Simplify 5 𝒄 −𝟑 + 𝟏𝟓 𝟏𝟓 𝟏𝟓 15 𝒄 −𝟑 𝒄 −𝟑 (-3) = c 1 Write the equation 2 Draw railroad tracks 3 Isolate the variable 4 Subtraction Property of Equality (subtract 15 from both sides of the equation) 5 Combine Like Terms/Simplify 6 Multiplication Property of Equality (multiply both sides of the equation by -3) 7 Simplify Solve by Combining Like Terms EXAMPLE: 𝟒𝒂 + 𝟑𝒂 = 𝟔𝟑 𝟒𝒂 + 𝟑𝒂 = 𝟔𝟑 1. Write the equation 2. Draw railroad tracks 𝟕𝒂 = 𝟔𝟑 𝟕𝒂 𝟔𝟑 = 𝟕 a 3. Combine Like Terms (4a+ 3a) 4. Isolate the variable 5. Division Property of Equality (Divide both sides of the equation by 7) 6. Simplify 𝟕 = 9 Equations with Negative Coefficients 4 Example: 𝟒 − 𝒙 − 𝑥 = 𝟏𝟎 𝟒 − 𝟏𝒙 = 𝟒 + (−𝟏𝒙) = -4 𝟏𝟎 𝟏𝟎 - 4 - 1x = −𝟏𝒙 = −𝟏 x = = 10 1. Write the equation 2. Train Tracks 3. Identity Prop. x = -1x 4. Subtraction Property 5. Subtraction Property of Equality (Subtract 4 from both sides of the equation 6. Simplify/Combine Like Terms 7. Division Property of Equality (Divide both side of the equation by –1) 8. Simplify 6 𝟔 −𝟏 -6 Combine Like Terms Before Solving 𝑚 − 5𝑚 + 3 = 47 Example: 𝑚 − 5𝑚 + 3 = 47 𝟏𝑚 − 5𝑚 + 3 = 47 − 𝟒𝒎 + 𝟑 = 𝟒𝟕 - 3 - 4m −𝟒𝒎 −𝟒 - 3 = 44 = m = Try It! 1. 2. 3. 37 = 4d + 5 8y + 6 – 9y = -4 𝑘 5 See Next Page − 10 = 3 𝟒𝟒 −𝟒 -11 1. Write the equation 2. Train Tracks 3. Identity Property m = 1m 4. Combine Like Terms 1m and 5m 5. Subtraction Property of Equality (Subtract 3 from each side of the equation) 6. Simplify/Combine Like Terms 7. Division Property of Equality (Divide both sides of the equation by – 4) 8. Simplify FUNCTIONS y is a function of x or y depends on x y = 3x - 15 Dependent variable Independent Variable Range Domain Output Input EXAMPLE: The output of a function is 2 more than 4 times the input. Find the input when the output is 14. Output is 2 more than “y” = “2 + “ 14 = 2 + 4x Solve the equation 14 = 4x + 2 14 -2 = 4x 12 12 4 = = 4x 4𝑥 4 3 = x + - 4 times input “4x” 2 2 TRY IT!! The output of a function is 3 less than 6 times the input. Find the input when the output is 15 Write an equation for the function. Let y be the output and x be the input “Is” means equal to, “more than” means to add, “times” means to multiply Substitute “14” in for the output “y” 1 Write the equation 2 Draw the railroad track 3 Isolate the variable 4 Subtraction Property of Equality (subtract 2 from each side of the equation 5 Combine Like Terms/Simplify 6. Division Property of Equality (divide both sides of the equation by 4) 7 Simiplify