"Absolute Value Inequality" is a type of mathematical inequality that represents the distance between a number and zero on a number line. It is denoted by vertical bars surrounding the number and is always equal to or greater than zero.
To solve absolute value inequalities, you must first isolate the absolute value expression on one side of the inequality. Then, you must consider two cases: when the expression inside the absolute value is positive and when it is negative. For each case, you can solve the inequality by removing the absolute value bars and solving for the variable.
The main difference between absolute value equations and inequalities is that equations have an equal sign, while inequalities have an inequality sign (such as <, >, ≤, ≥). Additionally, while equations have one unique solution, inequalities can have multiple solutions or a range of solutions.
Absolute value inequalities are important because they represent real-world scenarios where there is a distance or difference between two values. For example, they can be used to represent temperature changes, financial gains or losses, or any situation where the magnitude of a quantity is important.
Some common mistakes when solving absolute value inequalities include forgetting to consider both cases, incorrectly removing the absolute value bars, and forgetting to flip the inequality sign when multiplying or dividing by a negative number. It is important to carefully follow the rules of solving inequalities to avoid these mistakes.