Inequalities

Inequalities are mathematical expressions involving the symbols < (less than), ≤ (less than or equal to), > (greater than), or ≥ (greater than or equal to), and ≠ (not equal to).

In the context of an inequality, there are potentially multiple valid solutions, not just a single answer.

Inequalities can be solved similarly to equations, yet, whenever you multiply or divide both sides of an inequality by a negative number, the inequality symbol must be flipped.

If multiple inequalities are linked by the word ‘and’, then only the values that satisfy both inequalities are valid. This is referred to as the intersection of two sets.

When inequalities are combined by the word ‘or’, the solution will be all the values that satisfy either of the inequalities. This is called the union of two sets.

For a number line representation, exclusive inequalities (<, >) are denoted with an open circle, while inclusive inequalities (≤, ≥) with a closed circle.

When dealing with quadratic inequalities, you first need to make the inequality equal to zero and then solve the equation.

Unfamiliar and complex inequalities may sometimes be made simpler by substitifying (x = y^2).

Be careful about strict inequalities when square rooting both sides of an inequality.

Inequalities play a vital role in realworld scenarios such as business modelling, scientific research, and engineering.

Collectively, algebraic skills involving inequalities are fundamental to making reasoned decisions about ranges of possible values in diverse contexts.

Practice is essential to gaining proficiency in solving and applying inequalities. Solving a variety of inequality equations will help enhance logical thinking skills.

Always check your answers by substituting them back into the original inequality. If both sides of the inequality are true, then the solution is correct.

Never forget to write the solution in the format required in the instructions (e.g., in interval notation or as an inequality).