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Linear Inequalities

Secondary 2 practice

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Linear Inequalities practice questions

Secondary 2 topics, working towards the O-Level Mathematics 4052 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

Practise Linear Inequalities free

What this topic covers

Worked examples

Example 1

Solve 2(z−4)<−62(z - 4) < -6. State the largest integer value of z.
Show the worked solution
  • 2(z−4)<−62(z - 4) < -6
  • 2z−8<−6expand2z - 8 < -6 \quad \scriptsize\textit{expand}
  • 2z<−6+82z < -6 + 8
  • 2z<22z < 2
  • z<1z < 1
  • Largest integer value of z=0\text{Largest integer value of } z = 0

Answer: 00

Example 2

Given that x is a prime number satisfying 5x+5<935x + 5 < 93, find the largest such prime.
Show the worked solution
  • 5x+5<935x + 5 < 93
  • 5x<93−5subtract 5 from both sides5x < 93 - 5 \quad \scriptsize\textit{subtract 5 from both sides}
  • 5x<885x < 88
  • x<885x < \frac{88}{5}
  • x<1735x < 17\frac{3}{5}
  • The prime numbers less than 885\frac{88}{5} are: 2, 3, 5, 7, 11, 13, 17.
  • The largest prime value of xx is 17\boxed{17}.

Answer: 1717

Example 3

Ahmad scored 7171 and 8484 in the first two tests. By forming an inequality, find the minimum score Ahmad must obtain in the third test so that the average score for the three tests is at least 8484.
Show the worked solution
  • Let the score in the third test be xx.
  • 71+84+x3≥84\frac{71 + 84 + x}{3} \geq 84
  • 155+x≥252multiply both sides by 3155 + x \geq 252 \quad \scriptsize\textit{multiply both sides by 3}
  • x≥252−155x \geq 252 - 155
  • x≥97x \geq 97
  • The minimum score in the third test is 97\boxed{97}.

Answer: 9797

Questions parents ask

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The free plan is permanent and does not ask for a card. It has daily limits on the AI feedback, and the paid plans lift them.

Which syllabus does this follow?

O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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