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

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

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

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

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

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

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

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

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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