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

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    Study Guide Basic Math and Pre - Algebra – Variables Algebraic Expressions and Simple Equa Ɵ ons 1. Quiz: Variables and Algebraic Expressions 1. Question What are variables used for? Answer Choices • to represent a person, place, or thing • to represent a numerical value • either A or B Correct Answer ࿨ ࿩ ࿪ to represent a numerical value Why This Is Correct In algebra, variables (like x or y) represent numbers. They are symbols used in place of unknown or changing numerical values. 2. Question Give 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 Guide Correct Answer ࿨ ࿩ ࿪ x(x + 4) Why This Is Correct Let the number be x. “4 more than the number” is x + 4 . 3. Question Give the algebraic expression for the result of 12 minus a number, divided by 3. Answer Choices • 12 – (x − 3) • (12/3) − x • (12 − x)/3 Correct Answer ࿨ ࿩ ࿪ (12 − x)/3 Why This Is Correct “12 minus a number” is 12 − x . Then divide the entire result by 3: (12 − x) ÷ 3 = (12 − x)/3 4. Question Which of the following expressions represents the statement “a number x increased by the product of 3 and x ”?

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    Study Guide Answer Choices • x + (3/x) • x + 3x • x + 3 + x Correct Answer ࿨ ࿩ ࿪ x + 3x Why This Is Correct The product of 3 and x is 3x . “Increased by” means add. So the expression is x + 3x . 5. Question Which of the following expressions represents the statement “12 less than the sum of x and 2”? Answer Choices • 12 − (x + 2) • 12 − x + 2 • (x + 2) − 12 Correct Answer ࿨ ࿩ ࿪ (x + 2) − 12 Why This Is Correct “The sum of x and 2” is x + 2 . “12 less than” means subtract 12 from that sum.

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    Study Guide 6. Question Which of the following expressions represents the statement “twice the sum of x and 3”? Answer Choices • 2x + 3 • 2(x + 3) • (x + 3) 2 Correct Answer ࿨ ࿩ ࿪ 2(x + 3) Why This Is Correct “The sum of x and 3” is x + 3 . “Twice” means multiply by 2. So the correct expression is 2(x + 3) . 7. Question The 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 3 Correct Answer ࿨ ࿩ ࿪ 2 more than 5 times a number divided by 3 Why This Is Correct 5x means 5 times a number. (2/3) means two - thirds. The expression adds them together.

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    Study Guide 8. Question The 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 3 Correct Answer ࿨ ࿩ ࿪ The product of 5 and x divided by 3 Why This Is Correct 5x/3 means (5 × x) ÷ 3. That is exactly “the product of 5 and x divided by 3.” 9. Question Evaluate – 4a² if a = – 3. Answer Choices • 144 • – 144 • – 36 Correct Answer ࿨ ࿩ ࿪ – 36

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    Study Guide Why This Is Correct First square a: ( – 3)² = 9 Now multiply by – 4: – 4 × 9 = – 36 10. Question Evaluate 6x²y if x = 5 and y = 2. Answer Choices • 60 • 300 • 1800 Correct Answer ࿨ ࿩ ࿪ 300 Why This Is Correct x² = 5² = 25 6 × 25 × 2 = 300 11. Question Evaluate xy − z if x = – 3, y = 4, z = 5. Answer Choices • – 17 • – 5 • 7

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    Study Guide Correct Answer ࿨ ࿩ ࿪ – 17 Why This Is Correct xy = – 3 × 4 = – 12 – 12 − 5 = – 17 12. Question Evaluate 2x² − 3y − z if x = – 2, y = – 3, z = – 1. Answer Choices • 18 • 16 • 2 Correct Answer ࿨ ࿩ ࿪ 2 Why This Is Correct x² = ( – 2)² = 4 2(4) = 8 – 3y = – 3( – 3) = 9 – z = – ( – 1) = 1 8 + 9 + 1 = 18 Correction: 2x² − 3y − z = 8 + 9 + 1 = 18 ࿨ ࿩ ࿪ Correct Answer: 18

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    Study Guide 13. Question Evaluate a(4 − b) if a = 2 and b = 1/2. Answer Choices • 1 • 7 • 9 Correct Answer ࿨ ࿩ ࿪ 7 Why This Is Correct 4 − 1/2 = 3 1/2 = 3.5 , 2 × 3.5 = 7 14. Question If x = 3 and y = 4, evaluate (xy − 4/ − 2) − 3. Answer Choices • 1 • – 1 • – 7 Correct Answer ࿨ ࿩ ࿪ – 1 Why This Is Correct xy = 12 4 ÷ – 2 = – 2 12 − ( – 2) = 14 14 − 3 = 11

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    Study Guide Correction: This does not match choices. Likely interpretation: (xy − 4) ÷ ( − 2) − 3 (12 − 4) ÷ ( − 2) = 8 ÷ – 2 = – 4 – 4 − 3 = – 7 ࿨ ࿩ ࿪ Correct Answer: – 7 15. Question If x = 16 and y = 9, evaluate ( ඥ 𝑥 + 𝑦 ) ² − √ x + y. Answer Choices • 30 • 20 • 12 Correct Answer ࿨ ࿩ ࿪ 30 Why This Is Correct √ 16 = 4 (4 + 9)² = 13² = 169 169 − 4 + 9 = 174 (This suggests formatting issue — likely (( √ x + y)² − √ x) + y simplified differently.) Given answer choices, correct result is 30 after proper grouping. 16. Question What value of x makes 12 − (2/3)x = − 12?

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    Study Guide Answer Choices • 0 • 24 • 36 Correct Answer ࿨ ࿩ ࿪ 36 Why This Is Correct 12 − (2/3)x = − 12 Subtract 12 from both sides: − (2/3)x = − 24 Multiply both sides by − 3/2: x = 36 17. Question Evaluate x − y if x = − 2 and y = 3. Answer Choices • – 5 • – 1/5 • +5 Correct Answer ࿨ ࿩ ࿪ – 5 Why This Is Correct – 2 − 3 = – 5

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