MCQ Mathematics Chapter 5: LINEAR INEQUALITIES, HS 1st year

 

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1. Which of the following symbols represents an inequality?

A. $=$
B. $<$
C. $+$
D. $-$

Answer: B. $<$

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2. In the inequality $30x < 200$, which of the following is true for $x$ when $x$ is a natural number?

A. $x > 20$
B. $x = 20$
C. $x < 20/3$
D. $x = 10$

Answer: C. $x < 20/3$

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3. What happens to the inequality sign when both sides are multiplied or divided by a negative number?

A. It remains the same.
B. It is reversed.
C. It depends on the context.
D. It becomes an equation.

Answer: B. It is reversed.

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4. Solve the inequality $5x - 3 < 3x + 1$. The solution is:

A. $x > 2$
B. $x < 2$
C. $x = 2$
D. $x > -2$

Answer: B. $x < 2$

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5. Which of the following is an example of a strict inequality?

A. $3x + 2 \geq 5x - 4$
B. $x - 2 < 4$
C. $7x + 3 = 21$
D. $2x + 3 \leq 7$

Answer: B. $x - 2 < 4$

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6. What is the solution set for the inequality $4x + 3 < 6x + 7$?

A. $x > -2$
B. $x < -2$
C. $x \geq 2$
D. $x \leq 2$

Answer: A. $x > -2$

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7. If a student scores 62 and 48 marks in two tests, what is the minimum score required in the third test to achieve an average of at least 60 marks?

A. 65
B. 68
C. 70
D. 72

Answer: C. 70

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8. Which statement best describes a solution of an inequality?

A. It is a value that satisfies the equation.
B. It is a value that makes the inequality true.
C. It is always a single number.
D. It is always a positive number.

Answer: B. It is a value that makes the inequality true.

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9. In the inequality $ax + b < 0$, what type of inequality is this?

A. Strict inequality in one variable
B. Strict inequality in two variables
C. Slack inequality in one variable
D. Slack inequality in two variables

Answer: A. Strict inequality in one variable

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10. What does the solution set of the inequality $3x < 5$ represent when $x$ is a real number?

A. $x \in (-\infty, 5)$
B. $x \in (5, \infty)$
C. $x \in (-\infty, -5)$
D. $x \in [-5, 5]$

Answer: A. $x \in (-\infty, 5)$

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11. Solve the inequality $3(x - 1) \leq 2(x - 3)$. The solution is:

A. $x \leq -1$
B. $x \geq 1$
C. $x \leq 2$
D. $x \geq 4$

Answer: C. $x \leq 2$

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12. Which of the following inequalities represents a linear inequality in two variables?

A. $3x - 2y \geq 5$
B. $x^2 + y^2 \leq 9$
C. $2x + 3y = 7$
D. $x + y^2 > 4$

Answer: A. $3x - 2y \geq 5$

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13. What does the inequality $x + 2 \geq 0$ represent on a number line?

A. A shaded region to the left of 2.
B. A shaded region to the right of -2.
C. A circle at -2 and a shaded region to the left.
D. A circle at -2 and a shaded region to the right.

Answer: D. A circle at -2 and a shaded region to the right.

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14. The inequality $-8 \leq 5x - 3 < 7$ results in which solution for $x$?

A. $-1 \leq x < 2$
B. $x > 2$
C. $x < -1$
D. $-1 < x \leq 2$

Answer: A. $-1 \leq x < 2$

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15. Which of the following is the correct solution for the inequality $2x + 3 < 5x + 7$?

A. $x < 4$
B. $x < 2$
C. $x > 4$
D. $x \geq 4$

Answer: A. $x < 4$

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16. In the inequality $5x + 1 > -24$, the solution is:

A. $x > -5$
B. $x > -4$
C. $x < -5$
D. $x < -4$

Answer: A. $x > -5$

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17. The inequality $2x + 3 \leq 5x + 7$ simplifies to which of the following?

A. $x \geq -2$
B. $x \leq -2$
C. $x > 2$
D. $x < -2$

Answer: B. $x \leq -2$

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18. Solve the inequality $2(x - 3) > x + 5$. The solution is:

A. $x < 8$
B. $x > 8$
C. $x > -8$
D. $x < -8$

Answer: A. $x < 8$

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19. If a student’s marks in two unit tests are 70 and 75, what is the minimum mark they need in the third test to have an average of at least 80 marks?

A. 80
B. 85
C. 90
D. 100

Answer: B. 90

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20. A man wants to cut three pieces of wood from a 91 cm board. If the lengths of the pieces are $x$, $x + 3$, and $2x$, which of the following inequalities must hold to ensure that the total length of the pieces does not exceed 91 cm?

A. $x + (x + 3) + 2x \leq 91$
B. $x + (x + 3) + 2x = 91$
C. $x + (x + 3) + 2x \geq 91$
D. $x + (x + 3) + 2x = 90$

Answer: A. $x + (x + 3) + 2x \leq 91$

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21. In the inequality $3x + 2 < 5x - 4$, what is the solution for $x$?

A. $x > 3$
B. $x < -3$
C. $x < 3$
D. $x > -3$

Answer: B. $x < -3$

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22. What is the solution set for the inequality $5x - 3 \leq 3x + 1$?

A. $x \leq -2$
B. $x \geq 2$
C. $x \leq 2$
D. $x \geq -2$

Answer: C. $x \leq 2$

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23. Which of the following is the correct graphical representation of the solution to $x > 3$?

A. A shaded region to the left of 3.
B. A circle at 3 with a shaded region to the left.
C. A shaded region to the right of 3.
D. A circle at 3 with a shaded region to the right.

Answer: D. A circle at 3 with a shaded region to the right.

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24. Solve the inequality $4(x + 2) \leq 5(x + 1)$. The solution is:

A. $x \leq -1$
B. $x \geq 1$
C. $x \geq -1$
D. $x \leq 1$

Answer: C. $x \geq -1$

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25. What is the correct solution for the inequality $2x + 5 > 7x - 10$?

A. $x < 3$
B. $x > 3$
C. $x < -3$
D. $x > -3$

Answer: A. $x < 3$

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26. Which of the following is a strict inequality?

A. $x \leq 4$
B. $x > 2$
C. $x \geq 5$
D. $x = 6$

Answer: B. $x > 2$

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27. The inequality $5x + 6 \leq 3x + 10$ simplifies to which of the following?

A. $x \leq -2$
B. $x \geq -2$
C. $x \leq 2$
D. $x \geq 2$

Answer: A. $x \leq -2$

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28. In the system of inequalities $3x - 4 \leq 2x + 5$ and $5x + 2 \geq 12$, what is the solution for $x$?

A. $x \geq 7$
B. $x \geq -7$
C. $x \leq 7$
D. $x \leq -7$

Answer: B. $x \geq -7$

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29. Which of the following is a valid solution set for the inequality $x + 4 < 10$?

A. $x \in (-\infty, 6)$
B. $x \in (6, \infty)$
C. $x \in (-\infty, -6)$
D. $x \in (4, \infty)$

Answer: A. $x \in (-\infty, 6)$

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30. Solve the inequality $3x - 5 \geq 2x + 4$. What is the solution for $x$?

A. $x \geq -9$
B. $x \leq -9$
C. $x \geq 9$
D. $x \leq 9$

Answer: A. $x \geq -9$

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31. What is the solution set for the inequality $x - 7 > -2$?

A. $x > -9$
B. $x > 9$
C. $x \leq 9$
D. $x \geq -9$

Answer: A. $x > -9$

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32. In the inequality $3x + 5 \geq 11$, what is the solution for $x$?

A. $x \geq 2$
B. $x \geq -2$
C. $x > 2$
D. $x \leq 2$

Answer: A. $x \geq 2$

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33. Which of the following represents the solution to the inequality $2x + 4 \geq 10$?

A. $x \geq 3$
B. $x \leq 3$
C. $x \geq 4$
D. $x \leq 4$

Answer: A. $x \geq 3$

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34. If the inequality $2(x - 1) \geq x + 3$ holds, what is the solution for $x$?

A. $x \leq 4$
B. $x \geq 4$
C. $x \leq 1$
D. $x \geq 1$

Answer: A. $x \leq 4$

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35. If a student must get an average of at least 80 marks in 5 tests, and their marks in 4 tests are 75, 80, 85, and 90, what is the minimum marks they must score in the 5th test?

A. 70
B. 75
C. 80
D. 85

Answer: B. 75

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36. Solve the inequality $6x + 3 > 2x + 9$. The solution is:

A. $x > 1$
B. $x > -1$
C. $x < 1$
D. $x < -1$

Answer: A. $x > 1$

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37. What is the solution set for the inequality $7x - 4 \leq 2x + 11$?

A. $x \leq 3$
B. $x \geq 3$
C. $x \leq -3$
D. $x \geq -3$

Answer: A. $x \leq 3$

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38. The inequality $x + 5 > 12$ represents the solution set:

A. $x > 7$
B. $x < 7$
C. $x \geq 7$
D. $x \leq 7$

Answer: A. $x > 7$

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39. Solve the inequality $2x - 3 \geq 4x + 5$. The solution is:

A. $x \geq -4$
B. $x \leq -4$
C. $x \geq -5$
D. $x \leq -5$

Answer: B. $x \leq -4$

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40. Which of the following is the solution set for the inequality $4x + 1 < 2x + 9$?

A. $x > 4$
B. $x < 4$
C. $x > -4$
D. $x < -4$

Answer: B. $x < 4$

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41. In the inequality $-2x + 5 > 3x - 4$, the solution for $x$ is:

A. $x > 1$
B. $x < 1$
C. $x > -1$
D. $x < -1$

Answer: C. $x > -1$

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42. Solve the inequality $2(x + 4) < 3(x - 1)$. The solution is:

A. $x < 2$
B. $x < 4$
C. $x > 2$
D. $x > 4$

Answer: A. $x < 2$

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43. Which of the following represents the solution for the inequality $3x - 5 \geq 7x + 9$?

A. $x \geq -3.5$
B. $x \geq -4$
C. $x \leq -4$
D. $x \leq -3.5$

Answer: C. $x \leq -4$

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44. If the inequality $2(x - 3) > 5x - 6$ holds, the solution for $x$ is:

A. $x > 3$
B. $x < 3$
C. $x > 6$
D. $x < 6$

Answer: B. $x < 3$

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45. Solve the inequality $5(x + 2) \geq 3x + 12$. The solution is:

A. $x \geq 0$
B. $x \geq -2$
C. $x \geq 2$
D. $x \leq -2$

Answer: B. $x \geq -2$

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46. Which of the following is the solution for the inequality $7x - 9 \leq 3x + 7$?

A. $x \leq 4$
B. $x \geq 4$
C. $x \leq -4$
D. $x \geq -4$

Answer: A. $x \leq 4$

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47. Solve the inequality $4x + 5 \leq 3x + 10$. The solution is:

A. $x \leq -5$
B. $x \geq -5$
C. $x \leq 5$
D. $x \geq 5$

Answer: B. $x \geq -5$

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48. Which of the following is the correct representation of the solution to the inequality $x - 7 \geq 0$?

A. $x \geq 7$
B. $x \leq 7$
C. $x > 7$
D. $x < 7$

Answer: A. $x \geq 7$

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49. Solve the inequality $2x - 1 > 4x + 7$. The solution is:

A. $x > -4$
B. $x < -4$
C. $x > 4$
D. $x < 4$

Answer: B. $x < -4$

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50. What is the solution set for the inequality $3x - 4 \geq 2x + 3$?

A. $x \geq 7$
B. $x \leq 7$
C. $x \geq -7$
D. $x \leq -7$

Answer: A. $x \geq 7$

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51. Solve the inequality $5x + 3 > 4x + 7$. The solution is:

A. $x > -4$
B. $x < -4$
C. $x > 4$
D. $x < 4$

Answer: A. $x > -4$

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52. What is the solution for $2(x + 3) \geq 3(x - 1)$?

A. $x \leq 9$
B. $x \geq 9$
C. $x \geq -9$
D. $x \leq -9$

Answer: A. $x \leq 9$

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53. The inequality $-2(x - 4) \leq 3x + 2$ has a solution:

A. $x \geq -6$
B. $x \leq -6$
C. $x \geq 6$
D. $x \leq 6$

Answer: A. $x \geq -6$

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54. Solve $3(x - 2) > 2x + 4$. The solution is:

A. $x > 10$
B. $x < 10$
C. $x > -10$
D. $x < -10$

Answer: A. $x > 10$

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55. Which of the following is the solution for $-x + 5 \leq 7x - 9$?

A. $x \leq 2$
B. $x \geq 2$
C. $x \leq -2$
D. $x \geq -2$

Answer: B. $x \geq 2$

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56. Solve $2x - 7 > 3x - 4$. The solution is:

A. $x < -3$
B. $x > -3$
C. $x < 3$
D. $x > 3$

Answer: A. $x < -3$

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57. Solve $4(x - 1) \leq 2(2x + 3)$. The solution is:

A. $x \geq -5$
B. $x \leq -5$
C. $x \geq 5$
D. $x \leq 5$

Answer: D. $x \leq 5$

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58. Which of the following represents the solution for $3x - 8 > 5x - 4$?

A. $x > 2$
B. $x < 2$
C. $x > -2$
D. $x < -2$

Answer: B. $x < 2$

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59. Solve $7(x - 1) < 5(x + 3)$. The solution is:

A. $x > 8$
B. $x < 8$
C. $x > -8$
D. $x < -8$

Answer: B. $x < 8$

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60. The inequality $2x + 7 > 4(x - 3)$ simplifies to:

A. $x > 5.5$
B. $x < 5.5$
C. $x > -5.5$
D. $x < -5.5$

Answer: D. $x < -5.5$

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61. Solve $-3(x + 4) \leq 6 - 2x$. The solution is:

A. $x \geq -2$
B. $x \leq -2$
C. $x \geq 2$
D. $x \leq 2$

Answer: C. $x \geq 2$

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62. The inequality $5x - 9 \geq 3x + 7$ has the solution:

A. $x \geq 8$
B. $x \leq 8$
C. $x \geq -8$
D. $x \leq -8$

Answer: A. $x \geq 8$

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63. Solve $-4x + 5 < -3x + 8$. The solution is:

A. $x > 3$
B. $x < 3$
C. $x > -3$
D. $x < -3$

Answer: B. $x < 3$

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64. Which of the following is the solution for $-2x - 4 \geq 6$?

A. $x \leq -5$
B. $x \geq -5$
C. $x \leq 5$
D. $x \geq 5$

Answer: A. $x \leq -5$

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65. Solve the inequality $x - 4 \leq 2x + 7$. The solution is:

A. $x \leq -11$
B. $x \geq -11$
C. $x \leq 11$
D. $x \geq 11$

Answer: A. $x \leq -11$

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