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:

TASC_1701

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:

TASC_1702

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

tasc-lessthan-equal

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

TASC_1703

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

Pick test points from each region:

TASC_1704

This one is false.

TASC_1705

This one is true.

tasc-false-true

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

TASC_1706

This one is false.

So the solution for this inequality is

TASC_1707

About This Article

This article is from the book:

About the book authors:

Stuart Donnelly, PhD, earned his doctorate in mathematics from Oxford University at the age of 25. Since then, he has established successful tutoring services in both Hong Kong and the United States and is considered by leading educators to be one of the most experienced and qualified private tutors in the country. Nicole Hersey, PhD, is a lecturer at the University of Rhode Island, with a dual appointment to the School of Education and the Department of Mathematics. Ron Olson, MA, is an NBCT-certified teacher in Social Studies who teaches AP Government, Civics, and Contemporary World Problems at Clover Park High School in Lakewood, WA. In addition to his 35 years of teaching experience, he works as an AP US History workshop consultant for The College Board and has been the advisor for National Honor Society at his high school. Shannon Reed, MA, MFA, is a visiting lecturer at the University of Pittsburgh, where she teaches composition, creative writing, and business writing.

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