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