Junior Secondary · Mathematics

Inequalities: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Inequalities.

10 questions23 marksFree, no account

Question 1

1 mark

If $x$ is an integer satisfying the inequality $-2 \le x < 2$, how many possible values can $x$ take?

Question 2

1 mark

Solve the linear inequality:
$$2(x+3) - 5x \ge 4x + 15$$

Question 3

1 mark

Solve the linear inequality:
$$1 - \frac{x - 4}{3} < \frac{5x + 1}{6}$$
If $ x $ is an integer, determine the smallest possible value of $ x $.

Question 4

1 mark

Solve the inequality $5x - 12 > 18$.

Question 5

1 mark

Given that $ x $ is an integer satisfying both inequalities $ 2x - 5 < 3(x - 2) $ and $ \frac{k - 3x}{2} \ge 1 $, where $ k $ is a constant. If there are exactly 3 possible values for $ x $, which of the following describes the range of values of $ k $?

Question 6

2 marks

Solve the inequality $ x + 7 < 3 $ and state the result using an inequality sign.

Write your answer out first, then check it against the worked solution.

Question 7

3 marks

Solve the inequality $ 12 - 3x \le 6 $ and find the smallest integer value of $ x $ that satisfies this inequality.

Write your answer out first, then check it against the worked solution.

Question 8

5 marks

Solve the inequality $ \frac{3x-2}{5} - \frac{x+4}{2} > -2 $ and find the smallest integer value of $x$ that satisfies it.

Write your answer out first, then check it against the worked solution.

Question 9

5 marks

In a classroom, the number of girls is 5 more than twice the number of boys.

(a) If there are $b$ boys, express the number of girls in terms of $b$.

(b) The total number of students in the classroom must not exceed 35. Formulate an inequality to represent this situation in terms of $b$.

(c) Solve the inequality found in part (b).

(d) Given that the number of boys must be a whole number, what is the maximum possible number of boys in the classroom?

Write your answer out first, then check it against the worked solution.

Question 10

3 marks

If it is given that $ x + 3 < 10 $, find the possible range of the expression $ 2x - 1 $.

Write your answer out first, then check it against the worked solution.

* The content provided by thinka is generated by AI and may not always be accurate or up-to-date. Please use it as a supplementary resource and verify with official materials.

You've seen the model answer. Now get yours marked.

This page can show you how a good answer looks. It cannot tell you what your answer was missing. thinka marks your written work against the real mark scheme in about 15 seconds.

Get My Answers Marked Back to the notes

Want more questions like these? Get a fresh set on this topic, marked as you go.

Practise More