Rational Inequality

2( − 4)



< −4

1. Put the rational inequality in general

form.

()

()

> 0

where > can be replaced by <, ≤

≥

2. Write the inequality into a single

rational expression on the left side.(You can refer to the review section

for solving unlike denominators)

3. Set the numerator and denominator

equal to zero and solve. The values

you get are called critical values.

4. Plot the critical values on a number

line, breaking the number line into

intervals.

5. Substitute critical values to the

inequality to determine if the

endpoints of the intervals in the

solution should be included or not.

5. Select test values in each interval

and substitute those values into the

inequality.

Note:

If the test value makes the inequality

true, then the entire interval is a

solution to the inequality.

If the test value makes the inequality

false, then the entire interval is not a

solution to the inequality.

6. Use interval notation or set notation

to write the final answer.

( 0,

3

4

)



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