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Unit 2 Test A.4.b: Properties used to solve equations: Distributive Commutative Equality, Inverse, Identity Identify the properties that justify the work donebetween step 2 and step 3. Addition property of Equality. Distributive Property Additive Identity Additive Inverse Step 1: 3x + 5 = -1 Step 2: 3x + 5 + (-5) = -1 + (-5) Step 3: 3x + 0 = -6 Step 4: 3x = -6 Identify the property that justifies the work between steps 1 & 2. Division Property of Inequality Commutative Property Distributive Property Additive Inverse Step 1: 2(4 + x) ≥ -2 Step 2: 2(4 + x) ≥ -2 2 2 Identify the properties that justify each step. Step 1: 3x = -6Step 2: ⅓(3x) = ⅓(-6)Step 3: 1x = -2Step 4: x = -2 Between Step 1 & 2: Between Step 2 & 3: Between Step 3 & 4: Multiplicative Equality ? Multiplicative Inverse ? Multiplicative Identity ? Identify the properties that justify each step. 3(x + 1) = -12 given 3x + 3 = -12 3x + 3+(-3) = -12+(-3) 3x + 0 = -15 3x = -15 3x = -15 3 3 1x = -5 x = -5 Equality of Division ? Multiplicative Inverse ? Multiplicative Identity ? Equality of Addition ? Additive Inverse ? Additive Identity ? Distributive Property ? Identify the property that justifies the work between steps 1 & 2. Multiplication Property of Inequality Multiplication Property of Equality Distributive Property Additive Inverse Step 1: 2(3 + 2x) = 1Step 2: 6 + 4x = 1 Identify the property that justifies the work between steps 2 & 3. Division Property of Inequality Division Property of Equality Distributive Property Multiplicative Inverse Step 1: 2(4 + x) ≥ -2Step 2: 2(4 + x) ≥ -2 2 2Step 3: 1(4 + x) ≥ -2 Based on the Multiplicative Inverse property, fill in the blank. Step 1: 2x ≥ 10Step 2: ½(2x) ≥ ½(10)Step 3: x ≥ 5 Determine which property was incorrectly used forjustifying the steps and name the correct property that should have been used: Step 1 4x=-3 GivenStep 2 ¼(4x)=¼(-3) DistributiveStep 3 1x = -¾ Multiplicative InverseStep 4 x = -¾ Multiplicative Identity Step 2; Equality of Division Step 2; Equality of Multiplication Step 3; Multiplicative Identity Step 3; Additive Identity |