Linear Inequalities in Two Variables · 6.1.1

Representing situations as inequalities

Q: How do I know whether to use ≤ or <?

Check whether the boundary value itself is allowed. "At most" or "not more than" includes the limit, so use ≤. "Less than" or "fewer than" excludes it, so use the strict sign <. The exact wording of the situation tells you which symbol fits.

Q: Do I need two variables every time?

For this topic, yes. Situations here compare two related quantities, such as two types of items or two costs, so the inequality is written with two variables, x and y, representing those quantities.

Q: What if the situation mentions a fixed number of items available?

That fixed number becomes part of another inequality, such as x + y ≤ 20 for a total of at most 20 items available. This inequality may later be combined with others describing the same situation to form a system.

Pupils translate a described real-life situation, such as a budget or a capacity limit, into a linear inequality connecting two related quantities, x and y. This involves identifying the correct mathematical expression for each quantity and choosing the inequality symbol that matches the wording of the restriction given.

Written by the spmmath.com.my editorial team.

The official learning standard (6.1.1)

“Represent situations in the form of linear inequalities.”

What it means

How it is examined

Paper 1 may test writing a simple linear inequality from a short phrase. Paper 2 problem-solving questions usually begin with pupils forming a linear inequality in two variables from a described situation, which is then used in later parts of the question involving a system of inequalities.

Worked example

A canteen sells buns at RM2 each and drinks at RM1.50 each. Aini has at most RM30 to spend.

Write a linear inequality relating the number of buns, x, and the number of drinks, y, that she buys.

Cost of x buns = 2x. Cost of y drinks = 1.5y.
Total cost must not exceed RM30, so total cost ≤ 30.
Combine: 2x + 1.5y ≤ 30.

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

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Frequently asked questions

How do I know whether to use ≤ or <?

Check whether the boundary value itself is allowed. "At most" or "not more than" includes the limit, so use ≤.

"Less than" or "fewer than" excludes it, so use the strict sign <. The exact wording of the situation tells you which symbol fits.

Do I need two variables every time?

For this topic, yes. Situations here compare two related quantities, such as two types of items or two costs, so the inequality is written with two variables, x and y, representing those quantities.

What if the situation mentions a fixed number of items available?

That fixed number becomes part of another inequality, such as x + y ≤ 20 for a total of at most 20 items available. This inequality may later be combined with others describing the same situation to form a system.