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Unit 2 Test Review SOL. A.4.b The student will solve multi-step linear and quadratic equations and inequalities in two variables, including justifying steps used in simplifying expressions and solving equations and inequalities, using field properties and axioms of equality that are valid for the set of real numbers and its subsets. SOL A.4.d The student will solve multi-step linear and quadratic equations in two variables, including solving multi-step linear equations algebraically and graphically. SOL A.4.f The student will solve multi-step linear and quadratic equations in two variables,including solving real world problems involving equations. Between Step 1 & 2: Between Step 2 & 3: Between Step 3 & 4: Identify the properties that justify each step. Step 1: -8 = n + 3 Step 2: -8 - 3 = n + 3 - 3 Step 3: -11 = n + 0 Step 4: -11 = n Subtraction Property of Equality ? Additive Identity ? Additive Inverse ? Identify the property that justifies step 1 to step 2. Step 1: 13x -1=(12x+15)+7x Step 2: 13x - 1= 7x + (12x +15) Associative property of addition Identity property of addition Commutative property of addition Distributive property Between step 1 and step 2: Between step 2 and step 3: Between step 3 and step 4: Identify the properties that justify each step. Step 1: 2x = -8 Step 2: ½(2x) = ½(-8) Step 3: 1x = -4 Step 4: x = -4 Multiplicative Identity ? Multiplicative Inverse ? Equality of Multiplication ? Between step 1 and step 2: Between step 3 and step 4: Between step 4 and step 5: Identify the properties used to justify each step. Step 1: 2x = -3(4x - 2) + 1 Step 2: 2x = -12x + 6 + 1 Step 3: 2x = -12x +7 Step 4: 2x + 12x = -12x +12x + 7 Step 5: 14x = 0 + 7 Additive Inverse ? Equality Property of Addition ? Distributive Property ? What is the solution to 3(2x-1) = 3? x = What is the solution to: 2x-2 = -4 ? 3 x = What is the solution to: 3(2m-1) = 3m +12 m= What is the solution to: 4(x + 7) = 4x - 3 x = - 31 infinite solutions no solution x = 25 x = 0 x = 3 What is the solution to -5(2x-3) = -8x + 15 - 2x Infinite Solutions No Solution Select the algebraic expression that is represented by the algebra tiles below. 2x + 5 = -4x - 3 2x - 5 = -4x + 3 + + − − − − − -2x -5 = 4x +3 2x = 4 + + − − + − − 4 inches 10 inches The length of a rectangle is 4 inches more than its width. The perimeter of the rectangle is 40 inches. Select the two dimensions of the rectangle. 14 inches 12 inches 20 inches 8 inches The width of a rectangle is 3 inches less than its lenth. The perimeter of the rectangle is 54 inches. How many inches is the length of the rectangle? width = inches Length = 7 inches, Width = 9 inches Length = 10 inches, Width = 8 inches Length = 6 inches, Width =8 inches Length = 7 inches, Width = 5 inches The width of a rectangle is 2 inches more than its length. The perimeter of the rectangle is 32 inches. Select the correct length and width. The sum of three consecutive integers is -9. What are the three integers? Write them in order from least to greatest. The sum of three consecutive integers is 48. What are the three integers? Write them in order from least to greatest? The sum of three consecutive even integers is 24. What are the three integers? Write them below from least to greatest. |