Grade 7 Expressions & Equations Practice — Easy

Question 1 of 22Score 0/0Easy

Question 1 of 22: What is the distributive property?

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Keep going: Read the lesson: Factoring & Expanding Linear Expressions Factors, GCF & LCM Exponent Rules
Answer key for parents & teachers (22 questions)
  1. What is the distributive property? — a(b + c) = ab + ac. The distributive property states a(b + c) = ab + ac. Multiply the factor outside by each term inside.
  2. Expand: 4(3x + 2) — 12x + 8. 4 × 3x = 12x and 4 × 2 = 8. So 4(3x + 2) = 12x + 8.
  3. Expand: −2(5x − 3) — −10x + 6. −2 × 5x = −10x, −2 × (−3) = +6. So −2(5x − 3) = −10x + 6.
  4. What is the GCF of 8 and 12? — 4. Factors of 8: 1, 2, 4, 8. Factors of 12: 1, 2, 3, 4, 6, 12. Greatest common factor = 4.
  5. Factor 15x + 10 completely. — 5(3x + 2). GCF of 15 and 10 is 5. 15x + 10 = 5(3x + 2).
  6. Simplify: 5x + 3x − 2 — 8x − 2. Combine like terms: 5x + 3x = 8x. The −2 stays. Result: 8x − 2.
  7. Are 5x and 5x² like terms? — No, they have different exponents. Like terms must have the same variable AND the same exponent. 5x has x¹, 5x² has x², so they are NOT like terms.
  8. Which two terms are like terms? — 7a and −2a. 7a and −2a both have the variable a with exponent 1. They are like terms.
  9. Expand: (x + 4)(2) — note: just distributing 2 — 2x + 8. 2(x + 4) = 2x + 8.
  10. Is 4(x + 3) equivalent to 4x + 12? — Yes, by the distributive property. By the distributive property, 4(x + 3) = 4x + 4 × 3 = 4x + 12. They are equivalent.
  11. Solve: x + 7 = 15 — x = 8. Subtract 7 from both sides: x = 15 − 7 = 8.
  12. Solve: 3x = 24 — x = 8. Divide both sides by 3: x = 24 ÷ 3 = 8.
  13. Solve: 2x − 5 = 11 — x = 8. Add 5: 2x = 16. Divide by 2: x = 8.
  14. When you multiply both sides of an inequality by a negative number, you must: — Flip (reverse) the inequality sign. Multiplying or dividing by a negative number reverses the direction of the inequality.
  15. Solve: x/3 + 2 = 7 — x = 15. Subtract 2: x/3 = 5. Multiply by 3: x = 15.
  16. What does the solution to an inequality look like on a number line? — A ray or segment (range of values). An inequality has infinitely many solutions, shown as a ray (for >, <, ≥, ≤) or segment on the number line.
  17. What is the first step in setting up a word problem as an equation? — Identify the unknown and assign a variable. Always start by identifying what you do not know and giving it a variable name.
  18. Tickets cost $8 each. You spent $56. How many tickets did you buy? — 7 tickets. 8t = 56 → t = 7 tickets.
  19. A plumber charges $50 flat fee plus $40/hour. The total bill was $170. How many hours did he work? — 3 hours. 40h + 50 = 170 → 40h = 120 → h = 3 hours.
  20. A number is doubled, then 7 is subtracted. The result is 19. What is the number? — 13. 2n − 7 = 19 → 2n = 26 → n = 13.
  21. A candle is 12 cm tall and burns down 2 cm per hour. After how many hours is it 6 cm tall? — 3 hours. 12 − 2h = 6 → −2h = −6 → h = 3 hours.
  22. A babysitter earns $12/hour and has already saved $30. How many hours until she has $102? — 6 hours. 12h + 30 = 102 → 12h = 72 → h = 6 hours.