Solve the nonlinear inequality

A nonlinear inequality is a mathematical statement containing an inequality such as < or > and the expression does not describe a striaght line.

Solving the nonlinear inequality

Now that we have found the critical numbers, we can finish solving for x. The critical numbers are places where the function can change from the positive numbers to negative. In other words, the critical numbers show where the function changes between greater than zero and less than zero. If we test the intervals between the critical numbers we can see which are greater than zero and which are less than zero.


  • Solve Nonlinear Inequalities Algebraically
  • Find the critical numbers.
  • Graph the critical numbers on a number line.
  • Choose a number to test in each interval between the critical numbers.
  • Test these numbers in the inequality to see which produce true statements.
  • The intervals that produce true statements are the solutions.

An alternate way to solve nonlinear inequalities is by graphing. Remember a coordinate plane is simply two number lines set perpendicularly. By solving the inequality so that one side is zero and graphing the expression, the function can be compared with zero. The critical numbers are the zeros and the undefined values. The zeros occur at the x-intercepts

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