Inequalities such as $$\frac{3}{2x} > 1$$, $$\frac{2x}{x-3} < 4$$, $$\frac{2x-3}{x-6} \geq x$$, and $$\frac{1}{4} - \frac{2}{x^2} \leq \frac{3}{x}$$ are considered rational inequalities because each one contains at least one rational expression.

Claude

A rational inequality is an inequality that contains a rational expression. Examples of rational inequalities include $$\frac{3}{2x} > 1$$, $$\frac{2x}{x - 3} < 4$$, $$\frac{2x - 3}{x - 6} \geq x$$, and $$\frac{1}{4} - \frac{2}{x^2} \leq \frac{3}{x}$$. When solving a rational inequality, the standard techniques for solving linear inequalities are applied, with two important distinctions: the inequality sign must be reversed when multiplying or dividing by a negative number, and any values that make the rational expression undefined must be carefully considered and excluded.

Rational Inequality

https://openstax.org/details/books/intermediate-algebra-2e

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