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Inequality Calculator with steps | Inequality solver

Inequality Calculator

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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

Table of Contents

Instructions for using the Online Algebra Calculator

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.

Algebra Calculator with steps
Input user interface

The input user interface is subdivided into 4 parts according to their functionality, which are shown in figure 1.

  1. Input field: This is where you write the algrebraic expression you want to solve. You can do this using the keyboard of your device or the virtual keyboard of the calculator itself. You should use only the functions and operators that are presented in Table 1.
  2. Tool bar: From here you can perform the following three functions:
    1. Choose between degrees or radians
    2. Activate or deactivate trigonometric or hyperbolic functions on the virtual keyboard.
    3. Choose the variable for which you want to solve the entered equation.
  3. Virtual keyboard: In it are all the functions, constants and functions that you can use in the algebra calculator. Pressing the "Trig Frunctions" button on the tool bar displays the buttons for all trigonometric and hyperbolic functions.

Output interface

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.

Output interface


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.

Types of Inequalities

There are several types of inequalities:

  1. 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”.

  2. 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.

  3. 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.

  4. 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.

How to solve inequalities

Solving linear inequalities

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

Example: Solving quadratic inequalities

Solving quadratic inequalities

To solve quadratic inequalities, you must follow these steps:

  1. Write the quadratic inequality in standard form, e.g.: Ax² + Bx + C > 0
  2. Determine the critical points: to do so, find the solutions of the related quadratic equation.
  3. Use the critical points to determine the intervals where the inequality is correct. Write the solution in interval notation.

Example: Solve the quadratic inequality x² + 5x - 2 > 0

Solving quadratic inequalities example

How to solve absolute value inequalities

  1. To solve an absolute value inequality, split the inequality into two separate inequalities and solve them individually:
    • If the inequality has a greater than symbol (>), create two inequalities:
      • (expression inside absolute value) < -(number)
      • (expression inside absolute value) > (number)
    • The same logic applies for inequalities with "greater than or equal to" (≥).
  2. Similarly, if the inequality has a "less than" symbol (<), create two inequalities:
    • (expression within absolute value) < (number)
    • (expression within absolute value) > -(number)
  3. Solve each inequality. The solution is the union of the results.

Example: Solve the absolute value inequality |5x - 8| ≥ 3

Solving absolute value inequalities example

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