Inequalities Overview

Inequalities are mathematical statements used to compare expressions and include symbols like ‘<’, ‘>’, ‘≤’, and ‘≥’.
Unlike equations, inequalities define a range of solutions rather than a specific solution.

Solving Inequalities

Solving inequalities is like solving equations, with the goal to isolate the variable.
Use the BIDMAS order to undertake operations while solving the inequality.
For instance, to solve the inequality 3x > 12, divide both sides by 3 to get x > 4, means that all values of x greater than 4 satisfy the inequality.
Important to remember, when an inequality is multiplied or divided by a negative number, the inequality sign must be reversed.

Graphical Representation of Inequalities

Inequalities can be represented graphically.
A dashed line indicates a “less than” (<) or a “greater than” (>) inequality, meaning points on the line are not part of the solution.
A solid line is used for “less than or equal to” (≤) or “greater than or equal to” (≥) inequalities, meaning points on the line are included in the solution.
Shading is used to illustrate the solution set for the inequality.
For instance, region above the line is shaded when the y-value is greater than the x-value, and vice versa.

Compound Inequalities

Compound inequalities are two or more inequalities joined together by “and” or “or”.
When “and” is used, the solution of the inequality is where the solution sets of the two inequalities overlap.
When “or” is used, the solution set includes any solutions of either inequality.

Revision and Practice

Ensure you check your solutions by substitifying values into the original inequality to ensure it holds true.
Consistent practice in solving and graphing inequalities improves comprehension and proficiency. Apply different inequality problems to hone these skills.

Remember, inequalities provide a versatile tool for solving a variety of algebraic problems and understanding how different quantities relate and contrast to one another.