Linear Inequalities in Two Variables · Form 4

Turning everyday words into inequalities

Q: Which exact words in a question point to ≥, ≤, > or <?

"At least" and "not less than" both mean ≥, "at most" and "not more than" both mean ≤, while "more than" or "exceeds" mean strict >, and "fewer than" or "less than" mean strict <. Reading the exact phrase carefully, word by word, is what turns a sentence into the correct symbol.

Q: How do I turn a word problem into two variables and inequalities?

Give each unknown quantity a letter, usually x and y, based on what the question is comparing or limiting, then translate each condition sentence by sentence using the phrase-to-symbol list. Quantities like number of items or budget are usually also non-negative, so x ≥ 0 and y ≥ 0 are often needed too.

Q: What's a common mistake when converting words to inequalities?

Students often swap "at least" and "at most", writing ≤ instead of ≥ or vice versa, which flips the whole region. Another frequent slip is forgetting that real quantities like number of chairs or tickets cannot be negative, so x ≥ 0 and y ≥ 0 are missed even though the question implies them.

Phrases like 'at least', 'not more than', 'fewer than' each point to a particular symbol (≥, ≤, <), so understanding the exact meaning of the words is what lets you write the correct inequality for a situation.

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Words carry the direction and the edge

'At least 30' means the value can be 30 or more, so it becomes ≥ 30, with 30 itself allowed. 'Not more than 30' means 30 or fewer, so it is ≤ 30, again including 30.

'More than 30' and 'fewer than 30' both exclude 30 and become > 30 and < 30. The word tells you two things at once: which direction the values run, and whether the boundary number itself counts.

Why this understanding matters

Before you can draw any region, the situation must first be captured correctly as inequalities, and that step lives entirely in reading. A single word such as 'less' versus 'no less' flips the whole meaning, and choosing ≤ where the situation needs < quietly includes points that should be left out.

Getting the symbol right from the words is what makes everything drawn afterwards actually describe the real situation.

Traps in the wording

Watch for phrases that hide a boundary: 'maximum of 40' means ≤ 40, while 'exceeds 40' means > 40 with 40 excluded. Comparisons between two quantities also become inequalities 'there are at least twice as many chairs as tables' turns into y ≥ 2x.

A frequent slip is dropping the 'or equal to' part, writing < when the words allow the boundary value, or the reverse. Reading slowly and asking 'can the number itself happen?'

settles whether the edge is included.

Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)

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Frequently asked questions

Which exact words in a question point to ≥, ≤, > or <?

"At least" and "not less than" both mean ≥, "at most" and "not more than" both mean ≤, while "more than" or "exceeds" mean strict >, and "fewer than" or "less than" mean strict <. Reading the exact phrase carefully, word by word, is what turns a sentence into the correct symbol.

How do I turn a word problem into two variables and inequalities?

Give each unknown quantity a letter, usually x and y, based on what the question is comparing or limiting, then translate each condition sentence by sentence using the phrase-to-symbol list. Quantities like number of items or budget are usually also non-negative, so x ≥ 0 and y ≥ 0 are often needed too.

What's a common mistake when converting words to inequalities?

Students often swap "at least" and "at most", writing ≤ instead of ≥ or vice versa, which flips the whole region. Another frequent slip is forgetting that real quantities like number of chairs or tickets cannot be negative, so x ≥ 0 and y ≥ 0 are missed even though the question implies them.