Welcome to our Inequality Calculator! This powerful tool allows you to easily solve any inequality with just a few simple steps. Simply enter the inequality into the provided input field and hit the “Calculate” button. The Inequality Calculator will then provide you with a step-by-step solution.
Whether you’re a student trying to ace your math exams or a professional looking for a quick and accurate way to solve inequalities, our Inequality Calculator is the perfect tool for you. Give it a try now and see just how useful it can be!
|Valid functions and symbols||Description|
|log()||Logarithm base 10|
|sin(), cos(), tan(), csc(), sec(), cot()||Basic trigonometric functions|
|asin(), acos(), atan(), acsc(), asec(), acot()||Inverse trigonometric functions|
|sinh(), cosh(), tanh(), csch(), sech(), coth()||Hyperbolic functions|
|asinh(), acosh(), atanh(), acsch(), asech(), acoth()||Inverse hyperbolic functions|
|pi||PI number (π = 3.14159...)|
|e||Neper number (e= 2.71828...)|
|i||To indicate the imaginary component of a complex number.|
Table 1: Valid functions and symbols
In math, an inequality is a statement that compares the value of one expression to the value of another using one of the following inequality symbols:
Inequalities are used to describe situations where one value is not equal to another value. They are often used in algebra to describe conditions that must be met for a solution to be valid.
The solution to an inequality is a set of values that make the inequality true. For example, the solution to the inequality x + 3 < 5 is the set of all values of x that are less than 2 (since 5 – 3 = 2). The solution to the inequality y ≥ 10 is the set of all values of y that are greater than or equal to 10.
There are several types of inequalities:
Linear inequalities: These are inequalities that involve only one variable and can be represented in the form “ax + b < c” or “ax + b > c”, where a, b, and c are constants and x is the variable. An example of a linear inequality is “2x + 3 < 7”.
Quadratic inequalities: These are inequalities that involve a variable raised to the second power, such as “x2 + 2x + 1 < 0″. Quadratic inequalities can be solved by finding the values of x that make the inequality true and then testing those values to determine which ones are valid solutions.
Absolute value inequalities: These are inequalities that involve the absolute value of a variable, such as “|x – 3| < 4”. Absolute value inequalities can be solved by splitting them into two separate inequalities and solving each one separately.
Rational inequalities: These are inequalities that involve rational expressions, such as “1/x < 2”. Rational inequalities can be solved by finding the values of x that make the inequality true and then testing those values to determine which ones are valid solutions.
These are just a few examples of the types of inequalities that exist. There are many other types of inequalities that can be used in different mathematical contexts and in solving problems.
Most techniques for solving linear equations are applicable to the calculation of linear inequalities. Therefore, in order to find the solution to a real inequality, you can add or subtract any real number to both sides of an inequality, and you can also multiply or divide both sides by any positive real number to create equivalent inequalities.
To illustrate the above explained below I present how we can solve the following linear inequality:
To solve quadratic inequalities you must follow the following steps:
Example: Solve the quadratic inequality x2+5x-2>0
(expression inside absolute value) <- (number on the right side)
(expression inside absolute value) > (number on the right hand side).
The same setting is used for a greater than or equal to sign, >=.
(expression within absolute value) < (number on the right hand side)
(expression within absolute value) > – (number on the right hand side).
The same setting is used for inequality having a less than or equal to sign, <=.
Let’s see an example of how to solve an absolute value inequality :