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Published byEthel Allison Modified over 6 years ago

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Multi-Step Equations We must simplify each expression on the equal sign to look like a one, two, three step equation

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**Steps for solving multi-step equations**

If there are fractions, multiply by the LCD to cancel out the denominators Use the distributive property if necessary Combine Like terms Get the variables to one side of the = and the #’s on the other side Isolate the variable and solve Check your answer

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Combing Like Terms 10x – 3 - 4x + 4 = -2x x (10x - 4x) + (-3 + 4) = (-2x + 7x) + 3 6x + 1 = 5x x -5x 1x + 1 = x = 2 or x = 2 Practice: -5x = 18x -8x Answer: X = -26/15

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Practice 3x – 4x + 8 – 9 = 10 2x – 10 – 8x = 9 4x – 6x – 9x = 33 -4x + 8 – 10 = 12 4x – 3x + 7 = 12x – 6 -9 7 – 3x + 4x = 10 17 x – 10 – 4 = 15x X = -11 X = 19/-6 X = -3 X = -7/2 X = 2 X = 3 X = -7

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**Distributive Property**

-31x + 28 = x = X = 58/31 Practice: 3(x – 5) = x Answer: X = -1 -7(3x – 4) = 10(x -3) Distribute to get ride of the parentheses -21x + 28 = 10x – x -10x -31x + 28 = -30

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Practice 3(x – 6) = 10 -2(6x – 8) = -8 10 = 3(x + 4) 2(2x – 8) = 4(9 – 5x) 3(x – 8) + 10 = -5x 10 + 6x = -(3x – 9) 4x –(5x – 7) = 20 X = 28/3 X = 2 X = 4/3 X = 52/9 X = 7/4 X = -1/9 X = -13

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Fractions 6y – 3 = 4 6y = 7 6 Y = 7/6 Practice: ⅖ + ⅙y = -⅔y + ⅓ Answer: Y = -2/25 ¾y - ⅜ = ½ LCD = 8 (8)¾y – (8)⅜ = (8)½ 6y – 3 = 4

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**Solution? Solve the following problem 4x – 8 = 2(-4 + 2x)**

When an equation is an identity(true statement) our solution is all real numbers. Any real number you substitute into the equation will give you a true answer

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Example: 5(2-x) + 8x = 3(x - 6) When we have an equation with no variables and the statement is not true, our answer is no solution! There is no real number that will make our equation true

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