S OLVING O NE AND T WO S TEP E QUATIONS Algebra 1 Mr. Bise

S OLVING O NE -S TEP E QUATIONS To Solve an Equation, you will move terms from one side of the equal sign to the other. GOAL: Get the “x” (the variable) alone on one side of the equal sign. STRANGER DANGER! TOOL: Inverse Operations The Three Simplest Inverse Operations: Addition and Subtraction (Positive and Negative) Multiplication and Division (Multiply by the Reciprocal) Roots and Exponents

Addition & Subtraction (Positive and Negative) Equations

There is a house with two rooms One room has an “x” in it, the other does not x + 5 The wall between the rooms is where the “=“ sign is. = “x” wants to be completely alone in his room. So anyone else in that room is the Stanger Danger and has to be moved to the other room, BY YOU! 7 T HINK OF THE SITUATION LIKE THIS :

Identify who is in the “x” room that shouldn’t be there. The Stranger Danger: the “5” x + 5 = 7 Which operation ( +, -, x,  ) is attaching the “5” to the “x”? We must use the Inverse Operation Operation being used: “+” Inverse of “+”: “-”“-” So we must subtract 5 or add a negative 5 to get the “x” alone in his room. W E NEED TO GET THE “ X ” ALONE!

Subtract 5 from each side On the left, = 0 On the right, = 2 x = x = 2 Once the “x” is alone on one side, the other side is the answer. ANSWER: X + 5 = 7

Identify who is in the “x” room that shouldn’t be. Stranger Danger: the “8” x + 8 = 20 Which operation ( +, -, x,  ) is attaching the “8” to the “x”? We must use the Inverse Operation Operation being used: “+” Inverse of “+”: “-”“-” So we must subtract 8 or add a negative 8 to get the “x” alone in his room. W E N EED TO G ET THE “ X ” A WAY F ROM S TRANGER D ANGER !

Subtract 8 from each side On the left, = 0 On the right, = 12 x = x = 12 Once the “x” is alone on one side, the other side is the answer. ANSWER: X + 8 = 20

Identify who is in the “x” room that shouldn’t be. Stranger Danger: the “9” 15 = x - 9 Which operation ( +, -, x,  ) is attaching the “9” to the “x”? We must use the Inverse Operation Operation being used: “-” Inverse of “-”: “+”“+” So we must add 9 to get the “x” alone in his room. W E NEED TO GET THE “ X ” A WAY F ROM S TRANGER D ANGER

Add 9 to each side On the left, = 24 n the right, = = x = x Once the “x” is alone on one side, the other side is the answer. ANSWER: 15 = X - 9

Multiplication & Division Equations

Identify who is in the “x” room that shouldn’t be. Stranger Danger: the “2” 2x = 16 Which operation ( +, -, x,  ) is attaching the “2” to the “x”? We must use the Inverse Operation Operation being used: “●” Inverse of “●”: “”“” So we must divide by 2 to get the “x” alone in his room. W E NEED TO GET THE “ X ” A WAY F ROM S TRANGER D ANGER !

Divide each side by two On the left, 2 ÷ 2 = 1 On the right, 16 ÷ 2 = 8 x = 8 Once the “x” is alone on one side, the other side is the answer. ANSWER: 2x = X = 16

Identify who is in the “x” room Stranger Danger: the “2” x = 8 Which operation ( +, -, x,  ) is attaching the “2” to the “x”? We must use the Inverse Operation Operation being used: “  ” Inverse of “  ”: “●”“●” So we must multiply by 2 to get the “x” alone in his room. 2 W E NEED TO GET THE “ X ” A WAY F ROM S TRANGER D ANGER !

Multiply each side by 2 On the left, 2 ÷ 2 = 1 On the right, 8 x 2 = 16 x = 16 Once the “x” is alone on one side, the other side is the answer. ANSWER: x = (2)

Identify who is in the “x” room Stranger Danger: the “2/3” 2x = 1 Which operation ( +, -, x,  ) is attaching the “2/3” to the “x”? We must use the Inverse Operation Operation being used: “●” Inverse of “ ● ”: “÷”“÷” You Cannot Divide Fractions So we must multiply by the Reciprocal to get the “x” alone in his room. 3 W E NEED TO GET THE “ X ” A WAY F ROM S TRANGER D ANGER ! 2

Multiply each side by 3/2 On the left, 2/3 ● 3/2 = 1 On the right, 1/2 ● 3/2 = 3/4 x = 3/4 Once the “x” is alone on one side, the other side is the answer. ANSWER: 2x = x = ●●

E XIT T ICKET 1. x + 7 = x – 12 = x = = 5 5. x = x2x