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.

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. $y < 3$
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   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. $10y - 10 \ge 0$
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   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
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   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
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   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
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   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.

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