Solve a Rational Inequality | Solve 4x/(x-6) is less than 1 and write in interval notation
Channel: Minute Math
Date: 2022-01-11

In this video we learn how to solve Solve a Rational Inequality. We solve 4x/(x-6) is less than 1 and write the solution in interval notation.

The steps we follow on how to solve a rational inequality are:
1) Write the inequality as one quotient on the left and zero on the right.
2) Determine the critical points–the points where the rational expression will be zero or undefined.
3) Use the critical points to divide the number line into intervals.
4) Test a value in each interval. Above the number line show the sign of each factor of the numerator and denominator in each interval. Below the number line show the sign of the quotient.
5) Determine the intervals where the inequality is correct. Write the solution in interval notation.

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Marecek, L., & Mathis, A. H. (2020). Multiply and Divide Rational Expressions. In Intermediate Algebra 2e. OpenStax. https://openstax.org/books/intermediate-algebra-2e/pages/7-6-solve-rational-inequalities. License: CC BY 4.0. Access for free at https://openstax.org/books/intermediate-algebra-2e/pages/1-introduction