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Simultaneous Linear Inequalities

Secondary 3 practice

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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 3(x+2)≤123(x + 2) \leq 12 and 5x−7≥−125x - 7 \geq -12.
Show the worked solution
  • Solving the two inequalities separately,
  • 3(x+2)≤123(x + 2) \leq 12
  • 3x+6≤12expand3x + 6 \leq 12 \quad \scriptsize\textit{expand}
  • 3x≤12−63x \leq 12 - 6
  • 3x≤63x \leq 6
  • x≤63x \leq \frac{6}{3}
  • x≤2x \leq 2

Answer: −1<=x<=2-1 <= x <= 2

Example 2

Find the number of integer values of x that satisfy both 4(x+4)<544(x + 4) < 54 and 4x+7≥274x + 7 \geq 27.
Show the worked solution
  • Solve the first inequality: 4(x+4)<544(x + 4) < 54
  • x+4<544divide both sides by 4x + 4 < \frac{54}{4} \quad \scriptsize\textit{divide both sides by 4}
  • x+4<272x + 4 < \frac{27}{2}
  • x<272−4subtract 4 from both sidesx < \frac{27}{2} - 4 \quad \scriptsize\textit{subtract 4 from both sides}
  • x<192x < \frac{19}{2}
  • Solve the second inequality: 4x+7≥274x + 7 \geq 27
  • 4x≥27−7subtract 7 from both sides4x \geq 27 - 7 \quad \scriptsize\textit{subtract 7 from both sides}
  • 4x≥204x \geq 20

Answer: 55

Example 3

Sarah is buying durians at $15\$15 each. Sarah needs at least 66 durians for a gathering, but cannot spend more than $120\$120 in total. Find the possible numbers of durians Sarah can buy.
Show the worked solution
  • Let xx be the number of durians.
  • Since Sarah needs at least 66 durians:
  • x≥6⋯(1)x \geq 6 \quad \cdots (1)
  • Since the total cost must not exceed $120\$120:
  • 15x≤12015x \leq 120
  • x≤12015x \leq \frac{120}{15}
  • x≤8⋯(2)x \leq 8 \quad \cdots (2)
  • Combining (1)(1) and (2)(2): 6≤x≤86 \leq x \leq 8.

Answer: 6,7,86, 7, 8

Questions parents ask

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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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