 # What is a Two-Step Equation? An equation written in the form Ax + B = C.

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What is a Two-Step Equation? An equation written in the form Ax + B = C

a) 3x – 5 = 16 b) y/4 + 3 = 12 c) 5n + 4 = 6 d) n/2 – 6 = 4

1. Solve for any Addition or Subtraction on the variable side of equation by “undoing” the operation from both sides of the equation. 2. Solve any Multiplication or Division from variable side of equation by “undoing” the operation from both sides of the equation. PEMDAS in Reverse…

Addition  Subtraction Multiplication  Division

 Identify what operations are on the variable side. (Add, Sub, Mult, Div)  “Undo” each operation by using the opposite operation.  Whatever you do to one side, you must do to the other side to keep the equation balanced.

4x – 5 = 11 +5 = +5(Add 5 to both sides) 4x = 16(Simplify)  4 =  4(Divide both sides by 4) x = 4(Simplify)

2x – 5 = 17 3y + 7 = 25 5n – 2 = 38 12b + 4 = 28

x = 11 y = 6 n = 8 b = 2

x  3 + 4 = 9 - 4 = - 4 (Subtract 4 from both sides) x  3 = 5 (Simplify) (x  3)  3 = 5  3 (Multiply by 3 on both sides) x = 15(Simplify)

x  5 – 3 = 8 c  7 + 4 = 9  r  3 – 6 = 2  d  9 + 4 = 5

x = 55 c = 35 r = 24 d = 9

1. Make sure your equation is in the form Ax + B = C 2. Keep the equation balanced. 3. Use opposite operations to “undo” Follow the rules (PEMDAS in Reverse): 1.Undo Addition or Subtraction 2.Undo Multiplication or Division

What is a Multi-Step Equation? A multi-step equations takes more than two steps to solve. The same rules for two-step equations apply, but now you have equations that require you to do additional work BEFORE you begin to isolate the variable.

a) 8x - 3x - 10 = 20 b) 7x + 2(x + 6) = 39 c) (3x + 5) = -24

1. Start by simplifying one or both sides of the equation. This may require: a.Combining like terms b.Using the distributive property c.Multiplying by a reciprocal 2. Use inverse operations (PEMDAS in reverse) to isolate the variable.

8x – 3x – 10 = 20Original equation 5x – 10 = 20Combine like terms +10 = +10Add 10 to both sides 5x = 30Simplify  5 =  5Divide both sides by 5 x = 6Simplify

7x + 2(x + 6) = 39Original equation 7x + 2x + 12 = 39 Distributive property 9x + 12 = 39Combine like terms -12 = -12Subtract 12 from both sides 9x = 27Simplify  9 =  9Divide both sides by 9 x = 3Simplify

(3/2)(3x + 5) = -24Original equation · (2/3) = · (2/3)Multiply by reciprocal 3x + 5 = -16Simplify (-24/1 * 2/3 = -48/3 = -16) -5 = -5Subtract 5 from both sides 3x = -21Simplify  3 =  3Divide both sides by 3 x = -7Simplify

12v + 14 + 10v = 80 3 + 4(z + 5) = 31 5h + 2(11 – h) = -5 (3/2)(x – 5) = -6

v = 3 z = 2 h = -9 x = 1

 TB pp. 144-145 #1, 3, 7, 11, 15, 19, 21, 22, 25, 27, 31, 35, 40  TB pp. 150-151 #1, 5, 11, 13, 17, 18, 19, 23, 27, 31

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