Algebraic inequalities (other)

Algebraic inequalities are statements involving variables and the symbols $<$, $>$, $\leq$, or $\geq$, where the expressions on each side are algebraic (may include polynomials, rational expressions, or roots). 'Other' algebraic inequalities refers to those that do not fit the most common types (like linear or quadratic), such as those involving higher-degree polynomials, rational expressions, or absolute values.

Important properties

• To solve an algebraic inequality, find the values of the variable that make the inequality true.

• For rational inequalities, consider where the numerator and denominator are zero to find critical points.

• Inequalities can change direction when both sides are multiplied or divided by a negative number.

• Absolute value inequalities often split into two separate inequalities.