Linear Inequality in One Variable - SS2 Mathematics Lesson Note

Inequalities such as \(3x + 7 > 5\) are called linear inequalities in one variable \(x\). Solving them involving much the same steps as solving linear equations but here, a set of values as defined by the inequality operator form the solution to the linear inequality.

Example 1 Find the solution set of the inequality \(3x + 8 < 10 + 5x\)

Solution

\[3x + 8 < 10 + 5x\]

\[3x - 5x < 10 - 8\]

\(- 2x < 2\), note when dividing or multiplying by a negative number, the inequality sign reverses.

\[\frac{- 2x}{- 2} < \frac{2}{- 2}\]

\[x > - 1\]

The solution set consist of all numbers greater than \(- 1\).

Example 2 Solve the inequality \(2y - 2 \geq 10\)

Solution

\[2y - 2 \geq 10\]

\[2y \geq 10 + 2\]

\[2y \geq 12\]

\[y \geq \frac{12}{2}\]

\(y \geq 6\), i.e. the solution set consists of all numbers equal to 6 and greater than 6