初一英语数学方程求解步骤单选题40道

初一英语数学方程求解步骤单选题40道
1. Solve the equation: 2x + 5 = 11. What is the first step?
A. Add 5 to both sides
B. Subtract 5 from both sides
C. Divide both sides by 2
D. Multiply both sides by 2
答案：B。

本题考查一元一次方程求解的第一步。

原方程为2x + 5 = 11，第一步应是两边同时减去5，得到2x = 6。

选项A 是错误的，加5 会使方程变得更复杂。

选项C 是第二步，得到2x = 6 之后两边同时除以2 求出x。

选项D 也是错误的操作。

2. To solve the equation 3x - 7 = 8, what should you do first?
A. Add 7 to both sides
B. Subtract 7 from both sides
C. Multiply both sides by 3
D. Divide both sides by 3
答案：A。

此方程3x - 7 = 8，求解第一步应是两边同时加7，得到3x = 15。

选项B 会使方程错误。

选项C 和D 都不是第一步操作。

3. When solving the equation 4x + 9 = 21, which is the correct first step?
A. Subtract 9 from both sides
B. Add 9 to both sides
C. Divide both sides by 4
D. Multiply both sides by 4
答案：A。

对于方程4x + 9 = 21，首先应两边同时减去9，得到4x = 12。

选项B 操作错误。

选项C 是第二步。

选项D 不是正确的第一步。

4. Solve: 5x - 12 = 18. What is the initial step?
A. Add 12 to both sides
B. Subtract 12 from both sides
C. Multiply both sides by 5
D. Divide both sides by 5
答案：A。

方程5x - 12 = 18，第一步是两边同时加12，得到5x = 30。

选项B 会导致错误。

选项C 和D 都不是开始的步骤。

5. In the equation 6x + 8 = 26, what should be done first?
A. Subtract 8 from both sides
B. Add 8 to both sides
C. Divide both sides by 6
D. Multiply both sides by 6
答案：A。

对于方程6x + 8 = 26，首先要两边同时减去8，得到6x = 18。

选项B 是错误的。

选项C 是第二步。

选项D 不是正确的第一步操作。

6. Tom and Jerry bought some apples. Tom bought 5 apples and Jerry bought twice as many as Tom. If they spent $20 in total and each apple
costs $2, how many apples did they buy in total?
A. 10
B. 15
C. 20
D. 25
答案：B。

首先，Tom 买了5 个苹果，Jerry 买的是Tom 的两倍，即10 个。

所以总共买了15 个苹果。

A 选项10 只是Jerry 买的数量；C 选项20 不正确；D 选项25 数量过大。

7. A store sells two types of notebooks. Type A costs $3 each and Type
B costs $5 each. If a customer buys 5 notebooks of Type A and the total cost is $35, how many notebooks of Type B did the customer buy?
A. 2
B. 3
C. 4
D. 5
答案：C。

顾客买了5 本Type A 的笔记本，花费5×3 = 15 元。

总共花费35 元，所以买Type B 的花费是35 - 15 = 20 元，每本Type B 5 元，所以买了4 本。

A 选项2 本花费10 元，不够；B 选项3 本花费15 元，也不够；D 选项5 本花费25 元，超过了。

8. Mary and John are selling cookies. Mary sells each cookie for $2 and John sells each cookie for $3. If they sold a total of 15 cookies and earned $40, how many cookies did Mary sell?
B. 10
C. 12
D. 15
答案：B。

假设Mary 卖了x 个，John 卖了15 - x 个。

可得2x + 3(15 - x) = 40，解得x = 5，所以Mary 卖了10 个。

A 选项5 个是错误的计算结果；C 选项12 个不符合方程计算；D 选项15 个全部是Mary 卖的也不符合条件。

9. A school organized a field trip. Buses cost $500 each and vans cost $300 each. If they rented 5 vehicles in total and spent $2100, how many buses did they rent?
A. 2
B. 3
C. 4
D. 5
答案：A。

设租了x 辆巴士，5 - x 辆面包车。

则500x + 300(5 - x) = 2100，解得x = 3。

B 选项3 辆计算错误；C 选项4 辆不符合方程结果；D 选项5 辆全部是巴士花费会超过2100 元。

10. A toy store is having a sale. Dolls cost $10 each and cars cost $8 each. A customer bought a total of 12 toys and spent $100. How many dolls did the customer buy?
A. 4
C. 8
D. 10
答案：C。

设买了x 个娃娃，12 - x 个汽车。

则10x + 8(12 - x) = 100，解得x = 8。

A 选项4 个计算错误；B 选项6 个不符合方程计算；D 选项10 个数量过大。

11.Which of the following is the first step in solving the quadratic equation x² + 5x + 6 = 0?
A. Factoring
B. Completing the square
C. Using the quadratic formula
D. None of the above
答案：A。

本题考查一元二次方程求解的第一步。

因式分解是解决此类方程的常见方法之一，将方程化为(x + 2)(x + 3) = 0，从而得到方程的解。

12.For the quadratic equation 2x² - 8x = 0, the next step after factoring out 2x is:
A. x - 4 = 0
B. 2x(x - 4) = 0
C. x² - 4x = 0
D. 2(x² - 4x) = 0
答案：A。

先提取公因式2x 得到2x(x - 4) = 0，然后得到x - 4
13.In solving the quadratic equation x² - 9 = 0, the correct method is:
A. Factoring
B. Completing the square
C. Using the quadratic formula
D. Difference of squares
答案：D。

方程可以变形为(x + 3)(x - 3) = 0，这是利用平方差公式。

14.The quadratic equation x² + 2x - 3 = 0 can be solved by:
A. Only factoring
B. Only completing the square
C. Only using the quadratic formula
D. Any of the above methods
答案：D。

此方程可以通过因式分解、配方法、二次公式法来求解。

15.Which of the following is not a correct step in solving the quadratic equation x² + 6x + 9 = 0?
A. (x + 3)² = 0
B. x + 3 = 0
C. x = -3
D. x = 3
答案：D。

原方程变形为(x + 3)² = 0，解得x = -3，选项D 错
16. In solving the equation 2x + 5 = 11, if one mistakenly subtracts 5 from both sides first, which of the following will be the result?
A. 2x = 6
B. 2x = 16
C. 2x = -6
D. 2x = 1
答案：B。

解析：正确步骤应该是先在等式两边同时减去5，得到2x = 6。

如果先减去5 就变成了2x = 11 - 5 = 6，所以错误选项B 是错误的。

17. When solving the equation 3x - 7 = 8, if one adds 7 to the right side instead of both sides, which option is correct?
A. 3x = 15
B. 3x = 1
C. 3x = -1
D. 3x = 22
答案：D。

解析：正确的是在等式两边同时加7，得到3x = 15。

如果只在右边加7 就变成3x = 8 + 7 = 15，所以错误选项D 是错误的。

18. For the equation 4x + 9 = 21, if one divides by 4 on the left side first, what will happen?
A. x + 9 = 5.25
B. x + 2.25 = 21
C. 4x = 5.25
D. x + 9 = 21
答案：A。

解析：正确做法是先在等式两边同时减去9，再除以4。

如果先除以4 就变成x + 9 = 5.25，所以错误选项A 是错误的。

19. Solving the equation 5x - 3 = 12, if one subtracts 3 from 12 first, which is the outcome?
A. 5x = 15
B. 5x = 9
C. 5x = 3
D. 5x = 60
答案：C。

解析：应该先在等式两边同时加3，得到5x = 15。

如果先从12 中减去3 就变成5x = 9，所以错误选项C 是错误的。

20. In the equation 2x + 8 = 18, if one multiplies 2 on both sides first, what is the result?
A. x + 8 = 9
B. 4x + 8 = 36
C. 2x = 10
D. x + 8 = 36
答案：B。

解析：正确是先在等式两边同时减去8，再除以2。

如果先乘以2 就变成4x + 8 = 36，所以错误选项B 是错误的。

21. In solving the equation 2x + 5 = 11, the first step should be:
A. Add 5 to both sides
B. Subtract 5 from both sides
C. Multiply by 2 on both sides
D. Divide by 2 on both sides
答案：B。

本题考查方程求解的第一步。

原方程为2x + 5 = 11，为了得到2x 的值，应先减去5，所以第一步是从两边同时减去5。

选项 A 加5 是错误的。

选项 C 乘以2 和选项 D 除以2 都不是第一步应进行的操作。

22. When solving 3(x - 2) = 9, the correct first step is:
A. Divide both sides by 3
B. Add 2 to both sides
C. Expand the brackets
D. Subtract 2 from both sides
答案：C。

此方程中，首先应该将括号展开，即3x - 6 = 9。

选项A 除以3 不是第一步。

选项B 加2 和选项D 减2 都不是首先要进行的操作。

23. For the equation 4x - 7 = 13, the initial step is:
A. Add 7 to both sides
B. Subtract 7 from both sides
C. Multiply by 4 on both sides
D. Divide by 4 on both sides
答案：A。

原方程4x - 7 = 13，要得到4x 的值，第一步需两边
同时加7。

选项 B 减7 错误。

选项 C 乘 4 和选项 D 除4 都不是第一步。

24. To solve 2(x + 3) = 10, the first action is:
A. Multiply by 2 on both sides
B. Subtract 3 from both sides
C. Divide both sides by 2
D. Expand the brackets
答案：D。

这个方程首先要展开括号，得到2x + 6 = 10。

选项 A 乘2、选项B 减3 和选项C 除以2 都不是第一步应做的。

25. In the equation 5x + 8 = 23, the first step is:
A. Subtract 8 from both sides
B. Add 8 to both sides
C. Multiply by 5 on both sides
D. Divide by 5 on both sides
答案：A。

方程5x + 8 = 23，为求出5x 的值，第一步应两边同时减去8。

选项 B 加8 错误。

选项 C 乘 5 和选项 D 除5 都不是第一步。

26. In the equation 2x + a = 10, if x = 3 and the solution holds true, what is the value of a?
A. 2
B. 4
C. 6
答案：B。

因为x = 3，将其代入方程可得2×3 + a = 10，6 + a = 10，a = 10 - 6 = 4。

27. For the equation 5x - b = 20, when x = 5, which of the following is the correct value of b?
A. 5
B. 10
C. 15
D. 25
答案：A。

把x = 5 代入方程，5×5 - b = 20，25 - b = 20，b = 25 - 20 = 5。

28. Given the equation 3x + c = 18 and x = 4, find the value of c.
A. 6
B. 9
C. 12
D. 15
答案：C。

因为x = 4，所以3×4 + c = 18，12 + c = 18，c = 18 - 12 = 6。

29. In the equation 7x - d = 49, if x = 8, what is the value of d?
A. 7
B. 14
C. 21
答案：B。

由于x = 8，7×8 - d = 49，56 - d = 49，d = 56 - 49 = 7。

30. For the equation 4x + e = 32 and x = 7, determine the value of e.
A. 4
B. 8
C. 12
D. 16
答案：A。

把x = 7 代入方程，4×7 + e = 32，28 + e = 32，e = 32 - 28 = 4。

31. Which of the following is the correct simplification of the equation 2(x + 3) = 10?
A. 2x + 3 = 10
B. 2x + 6 = 10
C. 2x = 10 - 3
D. 2x = 10 - 6
答案：B。

本题考查乘法分配律的运用。

2(x + 3) 展开应是2x + 6，所以B 选项正确。

A 选项未正确使用乘法分配律，C 和D 选项变形错误。

32. When simplifying the equation 3x - 5 = 16, the first step should be:
A. Add 5 to both sides
B. Subtract 3x from both sides
C. Multiply both sides by 3
D. Divide both sides by 3
答案：A。

本题考查方程求解的第一步。

要使3x - 5 = 16 简化，应先在等式两边同时加上5，所以A 选项正确。

B 选项会使等式变形错误，C 和D 选项不是第一步操作。

33. In the equation 4(x - 2) = 12, after distributing, it becomes:
A. 4x - 2 = 12
B. 4x - 8 = 12
C. 4x = 12 + 2
D. 4x = 12 + 8
答案：B。

本题考查乘法分配律。

4(x - 2) 展开为4x - 8，所以B 选项正确。

A 选项未正确分配，C 和D 选项变形错误。

34. To solve the equation 2(3x + 1) = 18, the first step is to:
A. Divide both sides by 2
B. Multiply both sides by 2
C. Subtract 1 from both sides
D. Add 1 to both sides
答案：A。

本题考查方程求解的第一步。

对于2(3x + 1) = 18，第一步应先在等式两边同时除以2，得到3x + 1 = 9，所以 A 选项正确。

B 选项会使方程变得更复杂，C 和D 选项不是第一步操作。

35. The correct simplification of the equation 5(2x - 3) + 2 = 17 is:
A. 10x - 15 + 2 = 17
B. 10x - 3 + 2 = 17
C. 10x - 15 = 17 - 2
D. 10x - 3 = 17 - 2
答案：A。

本题考查乘法分配律。

5(2x - 3) 展开为10x - 15，所以 A 选项正确。

B 选项未正确使用乘法分配律，C 和D 选项变形错误。

36. Solve the equation: 2x + 5 = 17
A. x = 6
B. x = 7
C. x = 8
D. x = 9
答案：B。

本题先将5 移到等号右边得到2x = 17 - 5，即2x = 12，然后两边同时除以2，解得x = 6。

主要考查一元一次方程的求解步骤。

37. Find the value of x in the equation: 3(x - 2) = 15
A. x = 5
B. x = 6
C. x = 7
D. x = 8
答案：C。

先展开括号得到3x - 6 = 15，然后将6 移到等号右边得到3x = 15 + 6，即3x = 21，最后两边同时除以3，解得x = 7。

涉及去括号和移项的知识点。

38. Solve this equation: 4x - 3 = 2x + 9
A. x = 3
B. x = 4
C. x = 5
D. x = 6
答案：D。

先将2x 移到等号左边，得到4x - 2x = 9 + 3，即2x = 12，两边同时除以2 解得x = 6。

考查了移项和合并同类项的方法。

39. What is the solution of the equation: 2(x + 3) = 20
A. x = 7
B. x = 8
C. x = 9
D. x = 10
答案：A。

先展开括号得2x + 6 = 20，再将6 移到等号右边得2x = 20 - 6，即2x = 14，最后两边除以2 解得x = 7。

涵盖了展开括号和移项的运算。

40. Solve the equation: 5x + 8 = 3x - 4
A. x = -6
B. x = -4
C. x = -2
D. x = 0
答案：A。

将3x 移到等号左边得到5x - 3x = -4 - 8，即2x = -12，两边除以2 解得x = -6。

主要考查方程的移项和求解。