If you wish to solve absolute value inequalities, you must thoroughly understand the concept of the absolute value. Let's recall that the absolute value of x (which we denote by |x|) is the distance between this number and zero. In other words, if x is a real number, then:
- |x| = x if x is non-negative, and
- |x| = -x if x is negative.
For example:
- |-1| = 1;
- |0| = 0, and
- |11| = 11.
As you can see, it's really simple to notice and remember the rule: the absolute value of a non-negative number is just this number, while if the number is negative, we have to remember to erase the minus sign.
Now, absolute value inequality is any inequality that contains the absolute value of some expression. For instance, the inequality |x2 + 3x -18| < 3 involves a quadratic expression. Most often, however, we have to deal with absolute value inequalities containing linear expression, namely bx+c. In the most general form, they can be written as:
a * |bx + c| + d > e,
where the > can be, of course, replaced by <, ≤, or ≥. The most efficient way of dealing with such inequalities is… to use Omni's absolute value inequalities calculator 🙂. In what follows, we explain how it works before discussing how to solve absolute value inequalities by hand.
It is an undeniable fact that most students just hate math and find it the most challenging subject. You have to learn so many topics in a short span that it often becomes difficult to add another one to the list of already learned topics. In this situation, it is quite common to forget the finer points of a particular
topic/concept, and absolutely values are definitely one of those concepts that will land you in trouble if you don't give them the attention they deserve. In algebra, it is never easy to deal with absolutely values and that's for so many reasons. Most experts believe that the basic concept of absolutely values is not that difficult to comprehend, but it requires more interest and a deep understanding of the subject to manage inequalities as well as equations in a better way. You will also
have to understand how to plot graphs, and that's exactly when our absolutely value inequalities calculator will be of immense help. With the help of our absolute value calculator, you will be able to solve your equations and develop a better understanding of the whole concept. We charge you nothing for using our calculators and ensure that you get in a position to handle everything in the world of math from basic numeracy to linear algebra, advanced algebra, and calculus. To ensure
you find it easy to use our calculator, we've paid special attention to making the interface extremely simple. Use your keyboard to make entries, or use the menu at the top of the calculator to use mathematical operators. Save 15% on your first order! Use Discount code: MMD15 By using this absolute value equations calculator, you will find it extremely easy to manage things like trigonometric functions, exponents, matrices and
boundaries, and other types of algebraic problems. The feature of graph interface is also quite useful and allows you to visualize functions and calculate the gradients and do much more. So, what are you waiting for? Start using our absolute value calculator to make equations and inequalities a tad simpler.Deal with Absolute Values by Using the Absolute Value Calculator
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Solve inequalities
This calculator will try to solve the linear, quadratic, polynomial, rational, and absolute value inequalities. It can handle compound inequalities and systems of inequalities as well.
To graph inequalities, use the graphing calculator.
Your input: solve $$$2 \lt \left|{x - 1}\right| \leq 4$$$
Answer
Answer: $$$\left[-3, -1\right) \cup \left(3, 5\right]$$$
Approximate Form: $$$\left[-3, -1\right) \cup \left(3, 5\right]$$$