Absolute Value Inequalities Solving Graph Formula Examples Cuemath

Bonisiwe Shabane

-Oct 31, 2025, 8:14 AM

absolute value inequalities solving graph formula examples cuemath

Absolute value inequalities are inequalities in algebra that involve algebraic expressions with absolute value symbols and inequality symbols. In simple words, we can say that an absolute value inequality is an inequality with an absolute value symbol in it. It can be solved using two methods of either the number line or the formulas. An absolute value inequality is a simple linear expression in one variable and has symbols such as >, <, >, <. In this article, we will learn the concept of absolute value inequalities and the methods to solve them. We will mainly focus on the linear absolute value inequalities and discuss how to graph them with the help of various solved examples for a better understanding of the concept.

An absolute value inequality is an inequality that involves an absolute value algebraic expression with variables. Absolute value inequalities are algebraic expressions with absolute value functions and inequality symbols. That is, an absolute value inequality can be one of the following forms (or) can be converted to one of the following forms: So the absolute value inequalities are of two types. They are either of lesser than or equal to or are of greater than or equal to forms. The two varieties of inequalities are as follows.

In this section, we will learn to solve the absolute value inequalities. Here is the procedure for solving 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. In the picture below, you can see generalized example of absolute value equation and also the topic of this web page: absolute value inequalities . The diagram below illustrated the difference between an absolute value equation and two absolute value inequalities Enter any values for A,b and c for any absolute value equation |Ax + b| = c into the text boxes below and this solver will calculate your answer and show all of the...

Solve the absolute value inequality below: $$| x -1 | \ge 2 $$ Solve the absolute value inequality below: $$ |2x + 1| \lt 7 $$ Solve each of the following inequalities. Home » Algebra » Inequalities » Absolute Value Inequalities Absolute value inequality is a type of inequality that contains an absolute or mod (modulus) value sign with a variable inside it. The value of the variable represents its distance from the origin, which can be plotted on a number line.

Now, depending on whether the expression inside the modulus is positive or negative, there can be two possible cases: Suppose we consider the absolute value inequality |x| < 6. Here, the distance from the origin to the variable ‘x’ is less than 6 units. To solve |x| < 6, we follow the below steps. In this lesson, we are going to learn how to solve absolute value inequalities using the standard approach usually taught in an algebra class. That is, learn the rules and apply them correctly.

There are four cases involved when solving absolute value inequalities. CAUTION: In all cases, the assumption is that the value of “$a$” is positive, that is, $a > 0$. The absolute value of any number is either zero $(0)$or positive which can never be less than or equal to a negative number. The answer to this case is always no solution. The absolute value of any number is either zero $(0)$ or positive. It makes sense that it must always be greater than any negative number.

There are many opportunities for mistakes with absolute-value inequalities, so let's cover this topic slowly and look at some helpful pictures along the way. When we're done, I hope you will have a good picture in your head of what is going on, so you won't make some of the more common errors. Once you catch on to how these inequalities work, this stuff really isn't so bad. (Note: This lesson covers linear absolute-value inequalities only.) Recall the original definition of absolute values as distance: "| x | is the distance of x from zero." For instance, both −2 and +2 are two units from zero, as you can see... This means that their absolute values will both be 2; that is, we have:

Absolute Value Inequalities Solving Graph Formula Examples Cuemath

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