Simultaneous Linear Inequalities practice questions

Secondary 3 topics from 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 simultaneous linear inequalities free

What this topic covers

Worked examples

Example 1

Find the range of values of xx for which 4x−1≤x+24x - 1 \leq x + 2 and −20−3x≤−2-20 - 3x \leq -2.
Show the worked solution
  • Solvingthetwoinequalitiesseparately,Solving the two inequalities separately,
  • $4x - 1 \leq x + 2$
  • $4x - x \leq 2 + 1$
  • $3x \leq 3$
  • $x \leq \frac{3}{3}$
  • $x \leq 1$
  • $-20 - 3x \leq -2$

Answer: −6<=x<=1-6 <= x <= 1

Example 2

Find the smallest integer value of <i>x</i> satisfying both 2x−3>x+22x - 3 > x + 2 and 3x+24≥5x+43x + 24 \geq 5x + 4.
Show the worked solution
  • Solve the first inequality: $2x - 3 > x + 2$
  • $2x - x > 2 + 3 \quad \scriptsize\textit{collect like terms}$
  • $x > 5$
  • $x > 5 \quad \scriptsize\textit{divide both sides by 1}$
  • Solve the second inequality: $3x + 24 \geq 5x + 4$
  • $3x - 5x \geq 4 - 24 \quad \scriptsize\textit{collect like terms}$
  • $-2x \geq -20$
  • $x \leq 10 \quad \scriptsize\textit{divide by negative, reverse inequality}$

Answer: 66

Example 3

There are 2626 20-cent coins and 50-cent coins in a box. The total value of all the coins is more than \5.65,andthenumberof20−centcoinsisatleast, and the number of 20-cent coins is at least 3$ times the number of 50-cent coins. Find the possible numbers of 20-cent coins.
Show the worked solution
  • Let $x$ be the number of 20-cent coins.
  • Then the number of 50-cent coins is $26 - x$.
  • Since the number of 20-cent coins is at least $3$ times the number of 50-cent coins:
  • $x \geq 3(26 - x)$
  • $x \geq 78 - 3x \quad \scriptsize\textit{expand}$
  • $4x \geq 78$
  • $x \geq \frac{78}{4}$
  • $x \geq 19\frac{2}{4} \quad \cdots (1)$

Answer: 20,21,22,23,2420, 21, 22, 23, 24

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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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