TASC Math Exam—Solving Rational Inequalities

By Stuart Donnelly

The TASC Math exam will probably ask you to solve one or two rational inequality problems. To make the process easier, you should always include a number line in your solution.

Just like a rational number is two integers being divided, a rational expression is two polynomials being divided.

To solve a rational inequality problem, follow these steps:

  1. Get one side equal to 0.
  2. Simplify one side as much as possible.
    This may involve finding a lowest common denominator and combining like terms.
  3. Find the values that make the denominator equal to 0.
    These are restrictions on the domain and will be needed when determining the solution set.
  4. Solve for when the numerator equals 0 to determine other critical values.
  5. Set up a number line to check the different regions and determine which region or regions are your solution.

Here’s a sample problem:


So the denominator is x + 2, and the value of x that results in a value of zero is x = –2. Now for the numerator:


With this information, you can now draw a number line.


There’s still the potential of 3.5 to be included in the solution set because the inequality symbol is


On the other hand, –2 can’t be included because the denominator can never equal 0.

Pick test points from each region:


This one is false.


This one is true.


Now try a test point that’s greater than 3.5:


This one is false.

So the solution for this inequality is