Solving Linear Equations with Justification of Properties

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Solving Linear Equations with Justification of Properties PowerPoints must be narrated!

Let’s use properties to justify the steps we used to solve an equation. -2(x + 2) = 10 Step 1: -2x – 4 = 10 Distributive Property Step 2: +4 +4 Addition Property of Equality Step 3: -2x + 0 = 14 Additive Inverse Step 4: -2x = 14 Additive Identity Step 5: -2x = 14 Division Property of Equality -2 -2 Step 6: x = -7

Let’s use properties to justify the steps we used to solve an equation. 2(6x – 4) = 6 Step 1: 12x - 8 = 6 Distributive Property Step 2: +8 +8 Addition Property of Equality Step 3: 12x + 0 = 14 Additive Inverse Step 4: 12x = 14 Additive Identity Step 5: 12x = 14 Division Property of Equality 12 12 Step 6: 1x = 14/12 Multiplicative Inverse Step 7: x = 7/6 Multiplicative Identity

Step 3: -12x - 4 = 0 - 12 Additive Inverse Let’s use properties to justify the steps we used to solve an equation. -2(x + 2) = 10x - 12 Step 1: -2x – 4 = 10x - 12 Distributive Property Step 2: -10x -10x Subtraction Property of Equality Step 3: -12x - 4 = 0 - 12 Additive Inverse Step 4: -12x – 4 = -12 Additive Identity + 4 + 4 Step 5: -12x + 0 = - 8 Addition Property of Equality Step 6: -12 x = -8 Additive Inverse Step 7: -12x = -8 Additive Identity -12 -12 Step 8: 1x = -8/-12 Division Property of Equality Step 9: x = -8/-12 Multiplicative Inverse Step 10: x = 2/3 Multiplicative Identity

Fill in the blanks to justify the steps we used to solve an equation. -2(3x - 2) = x - 10 Step 1: -6x + 4 = x - 10 Distributive Property Step 2: -x -x Subtraction Property of Equality Step 3: -7x + 4 = 0 - 10 Additive Inverse Step 4: -7x + 4 = -10 Additive Identity - 4 - 4 Step 5: -7x + 0 = - 14 Subtraction Property of Equality Step 6: -7x = - 14 Additive Inverse Step 7: -7x = -14 Additive Identity -7 -7 Step 8: 1x = -14/-7 Division Property of Equality Step 9: 1x = 2 Multiplicative Inverse Step 10: x = 2 Multiplicative Identity

Now it is your turn! Journal Entry 1 15x + 1 = 9x - 5 Steps: Properties: