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GED Mathematical Reasoning Preparation Course：Expressions, equations and inequalities

不限时专题测验：关于Expressions, equations and inequalities的17道题，每道题作答后都有解释。每次题目和选项都会重新打乱。

  • 课程
  • 美国
  • 100道题
  • 核对于2026年10月13日
  • 事实核查：2026年10月13日
从课文开始GED Mathematical Reasoning Preparation: Lessons：阅读时间约420分钟。测试中的每道题在课文中都有讲解。

专题测验5：Expressions, equations and inequalities

  1. 第1题，共17题

    What is the value of 3x² − 2x + 5 when x = −2?
    显示答案

    答案: A. 21

    3(−2)² = 3 × 4 = 12. −2(−2) = +4. Then 12 + 4 + 5 = 21.

  2. 第2题，共17题

    A plumber charges $65 for a visit plus $90 for each hour of work. Which expression gives the cost for h hours?
    显示答案

    答案: A. 65 + 90h

    The $65 is charged once, and the $90 is charged for each of the h hours: 65 + 90h.

  3. 第3题，共17题

    Simplify: 4(x + 3) − 2(x − 5)
    显示答案

    答案: A. 2x + 22

    Distribute: 4x + 12 − 2x + 10. Note that −2 × −5 = +10. Combine: 2x + 22.

  4. 第4题，共17题

    Solve: 5x − 7 = 3x + 9
    显示答案

    答案: B. x = 8

    Subtract 3x from both sides: 2x − 7 = 9. Add 7: 2x = 16. Divide by 2: x = 8.

  5. 第5题，共17题

    Three consecutive whole numbers add up to 72. What is the smallest number?
    显示答案

    答案: C. 23

    Let the numbers be n, n + 1 and n + 2. Then 3n + 3 = 72, so 3n = 69 and n = 23.

  6. 第6题，共17题

    Plan A costs $30 a month plus $0.10 per minute. Plan B costs $45 a month with unlimited minutes. For how many minutes do the plans cost the same?
    显示答案

    答案: C. 150

    Set 30 + 0.10m = 45. Then 0.10m = 15, so m = 150 minutes.

  7. 第7题，共17题

    Solve the system: x + y = 12 and x − y = 4. What is x?
    显示答案

    答案: D. 8

    Add the two equations: 2x = 16, so x = 8. Then y = 12 − 8 = 4.

  8. 第8题，共17题

    A school sold 20 tickets for $190. Adult tickets cost $12 and child tickets cost $7. How many adult tickets were sold?
    显示答案

    答案: B. 10

    Let a + c = 20 and 12a + 7c = 190. Replace c with 20 − a: 12a + 140 − 7a = 190, so 5a = 50 and a = 10.

  9. 第9题，共17题

    Solve: 3x − 4 > 11
    显示答案

    答案: A. x > 5

    Add 4: 3x > 15. Divide by 3 (a positive number, so the sign stays): x > 5.

  10. 第10题，共17题

    Solve: −2x + 6 ≤ 14
    显示答案

    答案: C. x ≥ −4

    Subtract 6: −2x ≤ 8. Dividing by −2 flips the sign: x ≥ −4.

  11. 第11题，共17题

    Sam has $60. He pays $15 for a ticket and wants snacks that cost $4.50 each. What is the greatest number of snacks he can buy?
    显示答案

    答案: B. 10

    Write 15 + 4.50n ≤ 60. Then 4.50n ≤ 45, so n ≤ 10. He can buy at most 10 snacks.

  12. 第12题，共17题

    Multiply: (2x + 3)(x − 4)
    显示答案

    答案: A. 2x² − 5x − 12

    Multiply each term: 2x·x = 2x², 2x·(−4) = −8x, 3·x = 3x, 3·(−4) = −12. Combine: 2x² − 5x − 12.

  13. 第13题，共17题

    Factor: x² + 5x − 14
    显示答案

    答案: A. (x + 7)(x − 2)

    Find two numbers that multiply to −14 and add to 5: 7 and −2. So x² + 5x − 14 = (x + 7)(x − 2).

  14. 第14题，共17题

    Simplify: (x² − 16) ÷ (x + 4)
    显示答案

    答案: D. x − 4

    x² − 16 is a difference of squares: (x + 4)(x − 4). Divide out (x + 4) to get x − 4.

  15. 第15题，共17题

    Solve: x² − 6x + 8 = 0
    显示答案

    答案: D. x = 2 or x = 4

    Factor: (x − 2)(x − 4) = 0. A product is 0 only if a factor is 0, so x = 2 or x = 4.

  16. 第16题，共17题

    Use the quadratic formula to solve 2x² + 3x − 2 = 0.
    显示答案

    答案: B. x = 1/2 or x = −2

    a = 2, b = 3, c = −2. b² − 4ac = 9 + 16 = 25. x = (−3 ± 5) ÷ 4, so x = 2/4 = 1/2 or x = −8/4 = −2.

  17. 第17题，共17题

    The formula d = rt gives distance from rate and time. Which formula gives the time t?
    显示答案

    答案: C. t = d/r

    Divide both sides of d = rt by r: t = d/r. For example, 120 miles at 60 mph takes 2 hours.

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