Linear Equations and Linear Inequations Quiz - ICSE Class 8 Mathematics

Free practice quiz: Linear Equations and Linear Inequations (ICSE Class 8 Mathematics). 46 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This ICSE Class 8 Mathematics practice quiz has 46 multiple-choice questions on Linear Equations and Linear Inequations, and 46 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. If 5x + 7 = 2x + 22, then what is the value of x?

   1. 4
   2. 5
   3. 6
   4. 7
   Show answer

   Answer: B. 5

   Subtract 2x from both sides: 3x + 7 = 22. Subtract 7 from both sides: 3x = 15. Divide by 3: x = 5.

2. Which value of 'y' satisfies the inequality 10 - 2y >= 4?

   1. 1
   2. 2
   3. 3
   4. 4
   Show answer

   Answer: C. 3

   Subtract 10 from both sides: -2y >= -6. Divide by -2 and reverse the inequality sign: y <= 3. From the options, the integers that satisfy y <= 3 are 1, 2, and 3. The question asks for 'which value', implying a single correct choice among the options. Typically, such questions in Olympiads might ask for the largest possible value, or a value that satisfies. Given the options, 3 is the largest value that satisfies the condition. If the question intended 'largest integer', then 3 is the answer. If it intended 'any value', then 1, 2, and 3 are all valid. Assuming the intent is to test the boundary or the largest integer solution, the answer is 3.

3. The sum of three consecutive integers is 60. Find the largest integer.

   1. 19
   2. 20
   3. 21
   4. 22
   Show answer

   Answer: C. 21

   Let the smallest integer be x. The next two consecutive integers are x + 1 and x + 2. The equation is x + (x + 1) + (x + 2) = 60. Combine like terms: 3x + 3 = 60. Subtract 3: 3x = 57. Divide by 3: x = 19. The largest integer is x + 2, which is 19 + 2 = 21.

4. A number is increased by 15, and the result is multiplied by 2. If the final answer is 70, what is the original number?

   1. 20
   2. 25
   3. 30
   4. 35
   Show answer

   Answer: A. 20

   Let the original number be 'n'. The equation is 2(n + 15) = 70. Divide both sides by 2: n + 15 = 35. Subtract 15 from both sides: n = 20.

5. The difference between a number and 12 is 5. What is the number if it is greater than 12?

   1. 7
   2. 12
   3. 17
   4. 19
   Show answer

   Answer: C. 17

   Let the number be 'n'. The equation is |n - 12| = 5. Since the number is greater than 12, n - 12 is positive, so n - 12 = 5. Add 12 to both sides: n = 17.

More questions in this quiz

Answers and explanations are in the full quiz.

1. Solve for y in the equation: (y/3) + 2 = 7.
2. If 3(x - 2) = 18, find the value of x.
3. Which of the following is a solution to the inequality 2x - 5 > 9?
4. If the sum of a number and 9 is 23, what is the number?
5. What is the value of 'a' if 4a + 1 = 2a + 9?
6. Solve for m: (m/4) - 3 = 1.
7. If 7p - 3 = 4p + 12, find the value of p.
8. The sum of two consecutive even integers is 54. Find the smaller integer.
9. A number is such that when divided by 5 and then 3 is added to the result, the answer is 7. Find the number.
10. If 2(3x + 1) = 4(x + 3), what is the value of x?
11. The difference between two numbers is 15. If the larger number is x and the smaller number is 10, find x.
12. Solve for x: x/2 + x/3 = 5.
13. Which integer is NOT a solution to 4x + 5 <= 17?
14. If three times a number is decreased by 7, the result is 14. What is the number?
15. Find the value of k if 5(k + 2) - 3k = 14.
16. Solve the inequality: 2(x - 1) < x + 5.
17. If x is an integer such that 2x - 3 > x + 4, find the smallest possible value of x.
18. A number is doubled and then 5 is subtracted from the result. If the final answer is 19, what is the original number?
19. Solve for y: 1/y + 1/3 = 1/2.
20. The sum of the digits of a two-digit number is 11. If the digits are reversed, the new number is 9 less than the original number. Find the original number.
21. Which is the smallest integer greater than or equal to -5.5 that satisfies 3x + 10 >= -5?
22. If the perimeter of a rectangle is 40 cm, and its length is 8 cm more than its width, find the width.
23. Find the largest integer x such that 5x - 3 <= 2x + 9.
24. If y + 5 = 2(y - 3), find y.
25. The sum of two numbers is 50. One number is 10 more than the other. Find the larger number.
26. If 3(x - 5) >= 2(x - 3), find the smallest integer value of x.
27. A number is divided by 4, and the result is added to 5. If the total is 11, what is the number?
28. If 5x - 2 = 3x + 8, what is the value of x?
29. Solve for m: (m + 4) / 5 = 3.
30. Which integer is NOT a solution for the inequality 2x + 7 > 13?
31. The sum of two consecutive odd integers is 84. Find the smaller integer.
32. Solve for x: 1/4 + x/2 = 3/8.
33. Solve for x: 2x/5 + 1/5 = 3/5.
34. If 3(x + 2) = 4x - 5, find the value of x.
35. If a number is multiplied by 6, and then 8 is subtracted from the product, the result is 28. What is the number?
36. Solve for x: 3/x = 9/15.
37. If 2x + 5 = 4x - 3, what is the value of x?
38. The sum of three consecutive multiples of 5 is 105. Find the smallest multiple.
39. If 3(y - 1) - 2(y + 2) = 0, find y.
40. What is the value of x if x/3 - x/4 = 2?
41. If a number is increased by 10, and the result is divided by 3, the answer is 8. Find the number.

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