Notes: 1: Solve One Step & Two Step Equations: [ Unit: Solve Linear Equations] Definition: Inverse Operations: Addition _______________ [ positive ________________ ] Subtraction _______________ [ Negative ________________ ] Multiplication _______________ Division _______________ Example: "Undo Addition" + 5 = 8 What number goes in the box to make the statement true? x + 5 = 8 Example: "Move the TERM" Use the inverse operation for addition to "prove" your answer from above. MOVE THE TERM: "What you do to one side of the equal sign... "Undo Subtraction" "Move the TERM" - 5 = 8 What number goes in the box to make the statement true? x - 5 = 8 Use the inverse operation for subtraction to "prove" your answer from above. MOVE THE TERM: "What you do to one side of the equal sign... Example: "Undo a Negative" "Move the TERM" -5 + = -5 + x = 8 8 What number goes in the box to make the statement true? Use the inverse operation for a negative to "prove" your answer from above. MOVE THE TERM: "What you do to one side of an equal sign... Example: "Undo Multiplication" "Move the FACTOR" 5x = 30 What number does "x" have to be to make the statement true? 5 x = 30 Use the inverse operation of multiplication to "prove" your answer. Example: "Undo Division" "Move the FACTOR" x = 5 7 What number does "x" have to be to make the statement true? x 5 7 Use the inverse operation of division to "prove" your answer. = Example: Solve for x: x = + 9 4 In this problem we will move the ________ by using the inverse operation of ____________ To get x by itself, ___________ 9 from both sides of the equal sign. Example: Solve for x: - 7 + x = - 11 In this problem we will move the _________ by using the inverse operation of _____________ To get x by itself, ____________ 7 to both sides of the equal sign. Example: Solve for x: - 7 x = - 56 In this problem we will move the _________ by using the inverse operation of _____________ To get x by itself, ____________ both sides of the equal sign by _____. Example: Solve for x: x = 6 -7 In this problem we will move the _________ by using the inverse operation of _____________ To get x by itself, ____________ both sides of the equal sign by _____. 4th Grade: "Never divide by a fraction... _______________________________ Example: Solve for x: 1 3 x = -4 What is the factor multiplied to x ?____ What is the reciprocal of the factor ? _____ Multiply both sides by the reciprocal of the factor. Example: Solve for x: -2 3 x = -4 In this problem, we will move the __________ by _________________ both sides of the equal sign by the ________________ _____ . . Solve Two Step Equations: Two Steps: 1. 2. Example: Solve for x: "Move the TERM... Move the FACTOR..." 2x + 5 = 11 In this problem we will first move the _______ of ____ by _______________ from both sides of the equal sign. We will then move the _________ of ____ by __________ both sides of the equal sign by ___ . Example: Solve for x: "Move the TERM... Move the FACTOR..." - 4x - 5 = 11 In this problem we will first move the _______ of ____ by _______________ to both sides of the equal sign. We will then move the _________ of ____ by __________ both sides of the equal sign by ___ . Example: Solve for x: 3 2 x- 2= 7 "Move the TERM... Move the FACTOR..." In this problem we will first move the _______ of ____ by _______________ to both sides of the equal sign. We will then move the _________ of ____ by __________ both sides of the equal sign by the ____________ ___ . [ Unit: Solve Linear Equations] Notes: 1: Solve One Step & Two Step Equations: Definition: Inverse Operations: Addition Subtraction [ positive Negative ] Subtraction Addition [ Negative Positive ] Multiplication Division Division Multiplication Example: "Undo Addition" 3 + 5 = 8 "Move the TERM" What number goes in the box to make the statement true? zero pair x + 5 = 8 -5 -5 Use the inverse operation for addition to "prove" your answer from above. MOVE THE TERM: "What you do to one side of the equal sign... _ _ x=3 Example: "Undo Subtraction" "Move the TERM" 13 - 5 = 8 What number goes in the box to make the statement true? zero pair x - 5 = 8 +5 +5 Use the inverse operation for subtraction to "prove" your answer from above. MOVE THE TERM: "What you do to one side of the equal sign... _ _ x = 13 Example: "Undo a Negative" "Move the TERM" - 5 + 13 = 8 What number goes in the box to make the statement true? zero pair _ _ -5 + x = 8 +5 +5 x = 13 Use the inverse operation for a negative to "prove" your answer from above. MOVE THE TERM: "What you do to one side of an equal sign... Example: "Undo Multiplication" 5x = 30 _5 x What number does "x" have to be to make the statement true? x must be 6 because (5)(6) = 30 _ = 30 5 "Move the FACTOR" Use the inverse operation of multiplication to "prove" your answer. 5 x=6 Example: x = 5 "Undo Division" 7 "Move the FACTOR" What number does "x" have to be to make the statement true? x must be 35 because 35/5 = 7 x 5 = 7( 5 ( ( ( 15 Use the inverse operation of division to "prove" your answer. [ *note... (5/1) is the same as (5) ] x = 35 Example: Solve for x: x = + 9 _ 4 _ -9 -9 x=-5 Term In this problem we will move the ________ Addition by using the inverse operation of ____________ subtract To get x by itself, ___________ 9 from both sides of the equal sign. Example: Solve for x: - 7 + x = - 11 _ +7 _ +7 x = -4 Term In this problem we will move the _________ subtraction by using the inverse operation of _____________ Add To get x by itself, ____________ 7 to both sides of the equal sign. Example: Solve for x: _ _ - 7 x = - 56 -7 -7 Factor In this problem we will move the _________ Multiplication by using the inverse operation of _____________ x = - 13 To get x by itself, ____________ both sides of the divide -7 equal sign by _____. Example: Solve for x: x = 6 ( -7 -7 Factor In this problem we will move the _________ ( ( (-71 Division by using the inverse operation of _____________ x = - 42 To get x by itself, ____________ both sides of the multiply equal sign by _____. -7 4th Grade: multiply by the reciprocal" "Never divide by a fraction... _______________________________ (1 ( Example: Solve for x: 3 What is the factor multiplied to x ?____ ( 13 1 What is the reciprocal of the factor ? _____ ( x = - 4( 3 ( x = - 13 (3 ( 1 3 Multiply both sides by the reciprocal of the factor. Example: Solve for x: Factor In this problem, we will move the __________ (-32 multiplying by _________________ both sides of the equal x = 12 2 (-3 ( ( 1 (-32 x = -4 ( ( -2 3 2 reciprocal sign by the ________________ _____ . x= 6 . ( Solve Two Step Equations: Two Steps: 1. Move the TERM (add or subtract) 2. Move the FACTOR (multiply or divide) Example: Solve for x: "Move the TERM... Move the FACTOR..." 2x + 5 = 11 TERM In this problem we will first move the _______ _ _ 2x = _ 6 _ -5 -5 2 5 subtracting 5 of ____ by _______________ from both 2 sides of the equal sign. We will then move x = 3 2 the _________ by __________ both FACTOR of ____ dividing 2 . sides of the equal sign by ___ Example: Solve for x: "Move the TERM... Move the FACTOR..." - 4x - 5 = 11 TERM In this problem we will first move the _______ _ _ -_ 4x = 16 _ +5 +5 -4 - 5 by _______________ adding 5 of ____ to both -4 sides of the equal sign. We will then move x = -4 FACTOR of ____ - 4 by __________ dividing the _________ both -4 . sides of the equal sign by ___ Example: Solve for x: TERM In this problem we will first move the _______ +2 +2 3 x = 9 2 1 adding 2 - 2 by _______________ of ____ to both ( ( 32 sides of the equal sign. We will then move (3 ( x = 18 3 2 by __________ FACTOR of ____ multiplying both the _________ x= 6 3 . reciprocal sides of the equal sign by the ____________ ___ (2 ( ( ( 32 x- 2= 7 ( ( 3 2 "Move the TERM... Move the FACTOR..."
