Inequalities in one variable Quiz - ICSE Class 7 Mathematics

Free practice quiz: Inequalities in one variable (ICSE Class 7 Mathematics). 45 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This ICSE Class 7 Mathematics practice quiz has 45 multiple-choice questions on Inequalities in one variable, and 45 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. Solve for $y$: $3(y + 2) \ge 15$. Which of the following represents the solution set?

   1. $y \ge 3$
   2. $y \le 3$
   3. $y > 3$
   4. $y < 3$
   Show answer

   Answer: A. $y \ge 3$

   Divide both sides of the inequality by 3: $y + 2 \ge 5$. Subtract 2 from both sides: $y \ge 3$. The solution set is all values of $y$ greater than or equal to 3.

2. Which inequality is NOT equivalent to $10y - 4 \ge 6$?

   1. $10y \ge 10$
   2. $y \ge 1$
   3. $y > 1$
   4. $10y - 10 \ge 0$
   Show answer

   Answer: C. $y > 1$

   Start with the given inequality: $10y - 4 \ge 6$. Add 4 to both sides: $10y \ge 10$. This matches option A. Divide both sides by 10: $y \ge 1$. This matches option B. Let's check option C: $y > 1$. This is not equivalent to $y \ge 1$ because $y \ge 1$ includes $y=1$, while $y>1$ does not. Let's check option D: $10y - 10 \ge 0$. Add 10 to both sides: $10y \ge 10$. This is equivalent to the original inequality. Therefore, $y > 1$ is not equivalent.

3. Which value of $n$ satisfies $4n + 5 < 2n + 13$?

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

   Answer: A. 3

   Subtract $2n$ from both sides: $2n + 5 < 13$. Subtract 5 from both sides: $2n < 8$. Divide both sides by 2: $n < 4$. We need to find the value from the options that is less than 4. Option A (3) is less than 4. Option B (4) is not less than 4. Option C (5) is not less than 4. Option D (6) is not less than 4. Therefore, $n=3$ satisfies the inequality.

4. If $15 - 4p > 3$, what is the largest integer value of $p$?

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

   Answer: A. 2

   Subtract 15 from both sides of the inequality: $-4p > 3 - 15$, which simplifies to $-4p > -12$. Divide both sides by -4 and reverse the inequality sign: $p < -12 / (-4)$, which simplifies to $p < 3$. The largest integer value of $p$ that is strictly less than 3 is 2.

5. If $6 - 5x > 1$, what is the largest integer value of $x$?

   1. 0
   2. 1
   3. 2
   4. -1
   Show answer

   Answer: A. 0

   Subtract 6 from both sides of the inequality: $-5x > 1 - 6$, which simplifies to $-5x > -5$. Divide both sides by -5 and reverse the inequality sign: $x < -5 / (-5)$, which simplifies to $x < 1$. The largest integer value of $x$ that is strictly less than 1 is 0.

More questions in this quiz

Answers and explanations are in the full quiz.

1. If $-4m > 20$, what is the correct inequality for $m$?
2. Which integer is NOT a solution to the inequality $5x - 3 \le 12$?
3. For which value of $k$ is $3k + 7 > 16$ true?
4. What is the solution set for the inequality $10 - 3x \ge 1$?
5. If $5(2a - 1) < 35$, what is the largest integer value of $a$?
6. Solve for $z$: $7z + 3 \le 2z + 18$. What is the solution set?
7. Which of the following inequalities is equivalent to $2(x - 3) + 4x \le 30$?
8. If $\frac{m}{3} - 1 < 4$, what is the largest integer value of $m$?
9. If $5x - 3 > 2x + 6$, what is the smallest integer value of $x$?
10. The perimeter of a rectangle is less than 40 cm. If the length is 12 cm, what is the maximum possible integer width?
11. Solve for $p$: $15 - 2p \ge 5$. What is the solution set?
12. If $\frac{y}{5} + 3 > 7$, what is the smallest integer value of $y$?
13. If $\frac{x-2}{3} < 1$, what is the largest integer value of $x$?
14. Solve for $b$: $3b + 5 > 2b + 10$. What is the smallest integer value of $b$?
15. If $2x - 7 \le 5x + 8$, what is the correct inequality for $x$?
16. The sum of three consecutive integers is greater than 60. What is the smallest possible value of the smallest integer?
17. If $9 - \frac{x}{2} \le 4$, what is the smallest integer value of $x$?
18. If $x + 3 < 10$ and $x - 1 > 4$, what is the largest integer value of $x$?
19. If $12 - 5k \le 2$, what is the smallest integer value of $k$?
20. Which of the following is the solution set for $\frac{x}{2} + 1 \ge 4$?
21. Which integer does NOT satisfy the inequality $5x - 2 \le 13$?
22. If $20 - 3y \ge 5$, what is the largest integer value of $y$?
23. The cost of a notebook is $n$ dollars. If the cost of 3 notebooks and a pen is less than $20, and the cost of the pen is $2, what is the maximum possible integer cost of a notebook?
24. Solve for $x$: $7x + 2 \le 3x + 22$. What is the solution set?
25. If $\frac{x}{3} - 2 < 4$, what is the largest integer value of $x$?
26. Which inequality is NOT equivalent to $11b - 5 \ge 6b + 15$?
27. If $8 - 2x < 4$, what is the smallest integer value of $x$?
28. The sum of two consecutive odd integers is less than 70. What is the largest possible value of the smaller integer?
29. If $3(x + 4) \le 2x + 15$, what is the largest integer value of $x$?
30. Which integer does NOT satisfy the inequality $6y - 3 \ge 2y + 5$?
31. If $\frac{x}{4} - 1 \ge 2$, what is the smallest integer value of $x$?
32. Solve for $a$: $10a + 3 \le 7a + 18$. What is the solution set?
33. If $9x - 4 \le 5x + 12$, what is the correct inequality for $x$?
34. Solve for $z$: $20 - 4z \ge 8$. What is the solution set?
35. If $6k + 5 \le 2k + 21$, what is the largest integer value of $k$?
36. If $\frac{x+1}{2} \ge 5$, what is the smallest integer value of $x$?
37. Which inequality is NOT equivalent to $13m - 7 \ge 6m + 7$?
38. If $10 - 3k > 4$, what is the largest integer value of $k$?
39. If $3x + 7 \ge 4x - 1$, what is the correct inequality for $x$?
40. If $15 - 5k > 5$, what is the largest integer value of $k$?

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