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 −4m+4>−12-4m + 4 > -12. State the largest integer value of <i>m</i>.
Show the worked solution
  • $-4m + 4 > -12$
  • $-4m > -12 - 4$
  • $-4m > -16$
  • $m < \frac{-16}{-4} \quad \scriptsize\textit{divide by negative, flip sign}$
  • $m < 4$
  • $\text{Largest integer value of } m = 3$

Answer: 33

Example 2

Solve 21−3x>1121 - 3x > 11. Find the largest odd integer value of <i>x</i> that satisfies the inequality.
Show the worked solution
  • $21 - 3x > 11$
  • $-3x > 11 - 21 \quad \scriptsize\textit{subtract 21 from both sides}$
  • $-3x > -10$
  • $x < \frac{10}{3} \quad \scriptsize\textit{divide by negative, reverse inequality}$
  • $x < 3.3333$
  • The largest odd integer satisfying $x < \frac{10}{3}$ is $\boxed{3}$.

Answer: 33

Example 3

A gym membership costs a fixed fee of \43plus plus \99 per session. By forming an inequality, find the maximum number of sessions that can be attended while keeping the total cost within \148$.
Show the worked solution
  • Let the number of sessions be $n$.
  • $43 + 9n \leq 148$
  • $9n \leq 148 - 43$
  • $9n \leq 105$
  • $n \leq \frac{105}{9}$
  • $n \leq 11.67$
  • The maximum number of sessions is $\boxed{11}$.

Answer: 1111

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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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