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Mathematics · Class 9 · Chapter 6: Linear Equations and Inequalities

8 min

Key points

Linear equation in one variable has the form ax + b = 0, where a ≠ 0
Linear inequality symbols: < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to)
Solution of linear equation is the value of variable that satisfies the equation
Graphical representation of linear inequality shows solution set on number line
Properties of inequalities: Adding/subtracting same number preserves inequality direction
Multiplying/dividing by positive number preserves inequality direction
Multiplying/dividing by negative number reverses inequality direction
System of linear equations can be solved by substitution, elimination, or graphical method
Word problems involving linear equations follow: Read → Translate → Solve → Verify pattern

Definitions

Linear Equation: An equation in which the highest power of the variable is one is called a linear equation.
Linear Inequality: An inequality in which the highest power of the variable is one is called a linear inequality.
Solution Set: The set of all values of the variable that satisfy the given inequality is called the solution set.
System of Linear Equations: Two or more linear equations in the same variables considered together form a system of linear equations.
Consistent System: A system of equations that has at least one solution is called a consistent system.

Worked example

Solve the linear equation 3(x-2) = 2x + 4 and verify your answer. (4 marks)

The solution is x = 10. Verification confirms this is correct as both sides equal 24.

Common mistakes

Students forget to reverse inequality sign when multiplying/dividing by negative numbers
Not checking the solution by substituting back in original equation
Confusing inequality symbols (< vs ≤, > vs ≥)
In word problems, students fail to define variables clearly before setting up equations
Making arithmetic errors while solving system of equations

Quick recap

Linear equation in one variable has form ax + b = 0 where a ≠ 0. Solve by isolating variable through algebraic operations. Linear inequalities use <, >, ≤, ≥ symbols and solutions are represented on number line. Always verify solutions by substitution.

Generated by AI from Sindh Textbook Board material; review state: ai_unreviewed. MCQs, past-paper references and examiner notes are held back until a teacher has checked them.