In Class 7 mathematics ICSE, linear inequalities are introduced as a part of algebra. Here’s a summary:

– **Linear Inequality:** An inequality involving a linear expression in one or more variables is called a linear inequality.

– **Solving Linear Inequalities:**

– To solve a linear inequality, treat it as an equation and solve for the variable.

– Remember to reverse the inequality sign when multiplying or dividing by a negative number.

– **Graphical Representation:**

– Linear inequalities are often graphed on a number line.

– Use an open circle for < or > and a closed circle for ≤ or ≥, depending on whether the endpoint is included or not.

– **Interval Notation:**

– In interval notation, the solution set of a linear inequality is represented as an interval on the number line.

– **Word Problems:**

– Linear inequalities are used to represent real-life situations where a quantity is less than, greater than, less than or equal to, or greater than or equal to another quantity.

– **Example:** Solve the inequality 2x – 3 < 5.

– Add 3 to both sides: 2x < 8

– Divide by 2: x < 4

– The solution set is {x | x < 4}, represented as (-∞, 4) in interval notation.

This is a basic overview, and the actual curriculum may delve into more complex scenarios and applications of linear inequalities.