Solve Equations and Justify Each Step in the Solution

In this activity, you will work on algebraic proofs. Proving things are true is a very important skill to have as a mathematician! Be thinking about the "steps" in a proof. Also be thinking about how to justify each step. What property of numbers, or equality can be applied as reasons in your proof? 1. Which property is used to justify the following statement? Let a = 5 and b = 16. 2ab = 2(5)(16) = 160. Symmetric Property of Equality Reflexive Property of Equality Transitive Property of Equality Substitution Property of Equality 2. Which property justifies the work from Step 1 to Step 2 below? Step 1: 5x + 9 = 16 Step 2: 5x = 7 Subtraction Property of Equality Multiplication Property of Equality Division Property of Equality 3. Which property justifies the work from Step 1 to Step 2 below? Step 1: 7m = 63Step 2: m = 9 Addition Property of Equality Subtraction Property of Equality Division Property of Equality 4. Which property justifies the work from Step 1 to Step 2 below? Step 1: -8 + 6n = 4Step 2: 6n = 12 Multiplication Property of Equality Addition Property of Equality Division Property of Equality 5. Which property justifies the work from Step 1 to Step 2 below? Step 1: -x = 15Step 2: x = -15 Addition Property of Equality Subtraction Property of Equality Division Property of Equality 6. Fill in the missing parts of the proof by dragging the justifications to the correct step of the proof. 1. 4(x - 3) = 36 2. 4x - 12 = 36 3. 4x = 48 4. x = 12 STEPSAddition Property of Equality ? Division Property of Equality ? Distributive Property ? REASONSGiven Reflexive Property of = ? not used: 7. Fill in the missing parts of the proof by dragging the justifications to the correct step of the proof. 2. -6x + 12 = 24 3. -6x = 12 1. -6( x - 2 ) = 24 4. x = -2 STEPSSubtraction Property of = ? Distributive Property ? Division Property of = ? REASONSAssociative Property of = ? Given ? not used: 8. Fill in the missing parts of the proof by dragging the justifications to the correct step of the proof. 2. 6x – 3 = -21 3. 6x = -18 1. 8x - 3 = -21 + 2x 4. x = -3 STEPSSubtraction Property of = ? Division Property of = ? Addition Property of = ? REASONSAssociative Property of = ? Given ? not used: |

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