When the number on the other side of the inequality sign is negative, we either conclude all real numbers as the solutions, or the inequality has no solution.Solve the positive and negative versions of the absolute value inequality.Isolate on the left the absolute value expression.The following are the general rules to consider when solving absolute value inequalities: However, there is some extra information you need to keep in mind when solving absolute value inequalities. The steps for solving absolute value inequalities are much similar to solving absolute value equations. How to Solve Absolute Value Inequalities? So, the absolute value inequalities can possess any one of these four symbols. These are less than ( ), less than or equal ( ≤), and greater than or equal ( ≥). There are four different inequality symbols to choose from. For example, the expression |x + 3| > 1 is an absolute value inequality containing a greater than symbol. Now let’s see what the absolute value inequalities entail.Īn absolute value inequality is an expression with absolute functions as well as inequality signs. Absolute value is denoted by two vertical lines enclosing the number or expression.įor example, the absolute value of x is expressed as | x | = a, which implies that, x = +a and -a. What is Absolute Value Inequality?īefore we can learn how to solve absolute value inequalities, let’s remind ourselves about a number’s absolute value.īy definition, the absolute value of a number is the distance of a value from the origin, regardless of the direction.
This article will show a brief overview of the absolute value inequalities, followed by the step-by-step method to solve the absolute value inequalities.įinally, there are examples of different scenarios for better understanding. The difference is that we have a variable in the prior and a constant in the latter. The absolute value of inequalities follows the same rules as the absolute value of numbers.
Absolute Value Inequalities – Explanation & Examples
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