Rational Inequalities Calculator
Inequality is defined as an equation. In inequalities, you use less than, greater than, or not equal instead of an equal sign.
What is Rational Inequalities Calculator?
'Rational Inequalities Calculator' is an online tool that helps to find the value of x for a given inequality. Online Rational Inequalities Calculator helps you to find the value of x for a given inequality in a few seconds.
Rational Inequalities Calculator
How to Use Rational Inequalities Calculator?
Please follow the steps below on how to use the calculator:
- Step 1: Enter the rational inequality in the given input box.
- Step 2: Click on the "Solve" button to find the value of x for a given inequality.
- Step 3: Click on the "Reset" button to clear the field and enter new values.
How to Find Rational Inequalities?
A rational inequality is defined as an inequality such that it can be expressed as the rational expression, quotient, fraction p/q, or simply the quotient of two polynomials. It means both the numerator and denominator are polynomials.
There are different types of inequalities that are greater than(>), less than (<), greater than or equal to(≥), less than or equal to (≤). Rational inequality is a combination of rational expression and inequality.
For example x + 1 / x + 3 is a rational expression. x + 1 / x + 3 <= 5 is rational inequality.
Let us see an example to understand briefly.
Solved Examples on Rational Inequalities Calculator
Example 1:
Solve the rational inequality x + 5 / x + 3 >= 2
Solution:
\(\frac{(x + 5)}{(x + 3)} - 2 >=0\) \(\)[x + 3 is not equal to zero ⇒ x is not equal to -3]
\(\frac{(x + 5 - 2x - 6)}{(x + 3)} >=0\)
\(\frac{(-x - 1)}{(x + 3)} >=0\)
\(-x - 1>=0\\ x + 1<= 0\\ x<=-1\)
⇒ -3 < x <= -1
Example 2:
Solve the rational inequality x - 1 / x - 7 <= 5
Solution:
\(\frac{(x - 1)}{(x - 7)} - 5 <=0\) \(\)[x - 7 is not equal to zero ⇒ x is not equal to 7]
\(\frac{(x - 1 - 5x + 35)}{(x - 7)} <=0\)
\(\frac{(-4x + 34)}{(x - 3)} <=0\)
\(-4x + 34<=0\\ -4x <= -34\\ 4x>=34\\x>=34/4\\x>=17/2\)
Similarly, you can try the calculator to find the rational inequalities for:
- 5 < = 2x + 5 / x - 5
- x - 5 / 2x + 3 < 2