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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 |
---|---|
sqrt() | Square root |
ln() | Natural logarithm |
log() | Logarithm base 10 |
^ | Exponents |
abs() | Absolute value |
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
The algebra calculator has a very intuitive and friendly interface which makes it very easy to use. To explain in a simple way how to use it, we will first explain the elements of the input interface, through which you can enter the mathematical expressions you want to solve. Then we will explain the output interface, through which the calculator displays the solution.
The input user interface is subdivided into 4 parts according to their functionality, which are shown in figure 1.
The solution to the entered mathematical expression is displayed in the output interface. Depending on the nature of the mathematical problem, options may be generated to explore other variants of the solution. For example, if you've entered a quadratic equation, you'll be able to choose a different solving method, or if you've entered an equation with more than one variable, you'll be able to select which other variable you want to solve the equation for.
Valid functions and symbols
Valid functions and symbols | Description |
---|---|
sqrt() | Square root |
ln() | Natural logarithm |
log() | Logarithm base 10 |
^ | Exponents |
abs() | Absolute value |
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. |
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:
Example: Solve the inequality
To solve quadratic inequalities, you must follow these steps:
Example: Solve the quadratic inequality x² + 5x - 2 > 0
Example: Solve the absolute value inequality |5x - 8| ≥ 3