The representation of absolute value inequality is |ax + b | ), lesser than (), and lesser than or equal to ( and vice versa. The algebraic expressions are represented in absolute value symbol and the equals to symbol is replaced with greater than or less than symbol. We decide to use square brackets (or) parentheses for a number depending upon whether the given inequality has "=" in it.įAQs on Absolute Value Inequalities What are Absolute Value Inequalities in Algebra?Ībsolute value inequalities are inequalities in algebra that involve algebraic expressions with absolute value symbols and inequality symbols.We always use parentheses at -∞ or ∞ irrespective of the given inequality.If a square bracket is written at a number, it means that the number is included in the solution.If parenthesis is written at a number, it means that the number is NOT included in the solution.Important Notes on Absolute Value Inequalities |x| > -a or |x| ≥ -a ⇒ Set of all Real numbers, R. Thus, the solution to all such inequalities is the set of all real numbers, R. Thus the given two inequalities mean that "positive number is greater than (or greater than or equal to) negative number," which is always true. Also, -a is negative (as we assumed a is positive). We know that the absolute value always results in a positive value. Case 3: When the Inequality Is of the Form |x| -a or |x| > -a.
In this case, we use the following formulas to solve the inequality: If |x| > a ⇒ x a, and if |x| > a, then x a. Let us assume that a is a positive real number in all the cases.Ĭase 1: When the Inequality Is of the Form |x| a or |x| > a. There are 4 cases to remember for solving the inequalities using the formulas. To apply the formulas, first, we need to isolate the absolute value expression on the left side of the inequality. In fact, inequalities can be solved using formulas as well. This procedure works for any type of inequality. So far we have learned the procedure of solving the absolute value inequalities using the number line. The procedure to solve the absolute value inequality is shown step-by-step along with an example for a better understanding.Įxample: Solve the absolute value inequality |x+2| 4 ⇒ x ∈ (-∞, -6) U (2, ∞) Here is the procedure for solving absolute value inequalities using the number line. In this section, we will learn to solve the absolute value inequalities.
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