Linear Inequality in One Variable - JSS2 Mathematics Lesson Note

A linear inequality in one variable is similar to a linear equation but uses inequality symbols (<, >, ≤, ≥) instead of an equality sign (=). It represents a range of values rather than a single value.

General Form

A linear inequality in one variable can be written as:

𝑎𝑥+𝑏<𝑐

𝑎𝑥+𝑏>𝑐

𝑎𝑥+𝑏≤𝑐

𝑎𝑥+𝑏≥𝑐

where 

𝑎, 𝑏, and 𝑐 are constants, and 

𝑥 is the variable.

Examples:

2𝑥+3<7

−𝑥+5≥2

Solving Linear Inequalities

To solve a linear inequality:

• Isolate the variable on one side of the inequality.
• Perform the same operations on both sides of the inequality.

• If you multiply or divide both sides by a negative number, reverse the inequality sign.

   

Example 1: Solve 2𝑥+3<7

Subtract 3 from both sides:2𝑥<4

Divide both sides by 2:𝑥<2

Example 2: Solve −𝑥+5≥2

Subtract 5 from both sides:

−𝑥≥−3

Divide both sides by -1 (and reverse the inequality):

𝑥≤3