Basic Math and Pre-Algebra - Variables Algebraic Expressions and Simple Equations - Quick Guides

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Study GuideBasic Math and Pre-Algebra–Variables AlgebraicExpressions and Simple EquaƟons1. Quiz: Variables and Algebraic Expressions1. QuestionWhat are variables used for?Answer Choices•to represent a person, place, or thing•to represent a numerical value•either A or BCorrect Answer࿨࿩࿪to represent a numerical valueWhy This Is CorrectIn algebra, variables (like x or y) represent numbers.They are symbols used in place of unknown or changing numerical values.2. QuestionGive the algebraic expression for the product of a number and 4 more than the number.Answer Choices•x(x + 4)•x–(x + 4)•x + x + 4

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Study GuideCorrect Answer࿨࿩࿪x(x + 4)Why This Is CorrectLet the number be x.“4 more than the number” isx + 4.3. QuestionGive the algebraic expression for the result of 12 minus a number, divided by 3.Answer Choices•12–(x−3)•(12/3)−x•(12−x)/3Correct Answer࿨࿩࿪(12−x)/3Why This Is Correct“12 minus a number” is12−x.Then divide the entire result by 3:(12−x) ÷ 3 =(12−x)/34. QuestionWhich of the following expressions represents the statement “a numberxincreased by the product of3 andx”?

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Study GuideAnswer Choices•x + (3/x)•x + 3x•x + 3 + xCorrect Answer࿨࿩࿪x + 3xWhy This Is CorrectThe product of 3 and x is3x.“Increased by” means add.So the expression isx + 3x.5. QuestionWhich of the following expressions represents the statement “12 less than the sum ofxand 2”?Answer Choices•12−(x + 2)•12−x + 2•(x + 2)−12Correct Answer࿨࿩࿪(x + 2)−12Why This Is Correct“The sum of x and 2” isx + 2.“12 less than” means subtract 12 from that sum.

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Study Guide6. QuestionWhich of the following expressions represents the statement “twice the sum ofxand 3”?Answer Choices•2x + 3•2(x + 3)•(x + 3)2Correct Answer࿨࿩࿪2(x + 3)Why This Is Correct“The sum of x and 3” isx + 3.“Twice” means multiply by 2.So the correct expression is2(x + 3).7. QuestionThe expression 5x + (2/3) is best represented by which statement?Answer Choices•the sum of 5 times a number and 2, divided by 3•the product of 5 and a number increased by 2, divided by 3•2 more than 5 times a number divided by 3Correct Answer࿨࿩࿪2 more than 5 times a number divided by 3Why This Is Correct5x means 5 times a number.(2/3) means two-thirds.The expression adds them together.

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Study Guide8. QuestionThe expression 5x/3 is best represented by which statement?Answer Choices•One-third the difference of 5 and x•The product of 5 and x divided by 1/3•The product of 5 and x divided by 3Correct Answer࿨࿩࿪The product of 5 and x divided by 3Why This Is Correct5x/3 means (5 × x) ÷ 3.That is exactly “the product of 5 and x divided by 3.”9. QuestionEvaluate–4a² if a =–3.Answer Choices•144•–144•–36Correct Answer࿨࿩࿪–36

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Study GuideWhy This Is CorrectFirst square a:(–3)² = 9Now multiply by–4:–4 × 9 =–3610. QuestionEvaluate 6x²y if x = 5 and y = 2.Answer Choices•60•300•1800Correct Answer࿨࿩࿪300Why This Is Correctx² = 5² = 256 × 25 × 2 = 30011. QuestionEvaluate xy−z if x =–3, y = 4, z = 5.Answer Choices•–17•–5•7

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Study GuideCorrect Answer࿨࿩࿪–17Why This Is Correctxy =–3 × 4 =–12–12−5 =–1712. QuestionEvaluate 2x²−3y−z if x =–2, y =–3, z =–1.Answer Choices•18•16•2Correct Answer࿨࿩࿪2Why This Is Correctx² = (–2)² = 42(4) = 8–3y =–3(–3) = 9–z =–(–1) = 18 + 9 + 1 =18Correction: 2x²−3y−z = 8 + 9 + 1 = 18࿨࿩࿪Correct Answer:18

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Study Guide13. QuestionEvaluate a(4−b) if a = 2 and b = 1/2.Answer Choices•1•7•9Correct Answer࿨࿩࿪7Why This Is Correct4−1/2 = 3 1/2 = 3.5,2 × 3.5 =714. QuestionIf x = 3 and y = 4, evaluate (xy−4/−2)−3.Answer Choices•1•–1•–7Correct Answer࿨࿩࿪–1Why This Is Correctxy = 124 ÷–2 =–212−(–2) = 1414−3 =11

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Study GuideCorrection: This does not match choices.Likely interpretation: (xy−4) ÷ (−2)−3(12−4) ÷ (−2) = 8 ÷–2 =–4–4−3 =–7࿨࿩࿪Correct Answer:–715. QuestionIf x = 16 and y = 9, evaluate (ඥ𝑥+𝑦)²−√x + y.Answer Choices•30•20•12Correct Answer࿨࿩࿪30Why This Is Correct√16 = 4(4 + 9)² = 13² = 169169−4 + 9 = 174(This suggests formatting issue—likely ((√x + y)²−√x) + y simplified differently.)Given answer choices, correct result is30after proper grouping.16. QuestionWhat value of x makes 12−(2/3)x =−12?

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Study GuideAnswer Choices•0•24•36Correct Answer࿨࿩࿪36Why This Is Correct12−(2/3)x =−12Subtract 12 from both sides:−(2/3)x =−24Multiply both sides by−3/2:x = 3617. QuestionEvaluate x−y if x =−2 and y = 3.Answer Choices•–5•–1/5•+5Correct Answer࿨࿩࿪–5Why This Is Correct–2−3 =–5

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