3. Solving Non-linear Inequalities
Another method of solving inequalities is to express the given inequality with zero on the right side and then determine the sign of the resulting function from either side of the root of the function.
The steps are as follows:
- Rewrite the inequality so that there is a zero on the right side.
- Find all linear factors of the function.
- To find the critical values, set each linear function to zero and solve for x.
- Determine the sign of the function in the intervals formed by the critical values.
- The solution will be those intervals in which the function has the correct signs satisfying the inequality.
Example 1:
Solve the inequality x2 − 3 > 2x
Example 2:
Solve the inequality x3- 4x2 + x + 6 < 0
Example 3:
Solve the inequality 
Exercises
1. Solve x3- 2x2 + x ≥ 0
2. The mass m, in Mg, of fuel in a rocket after launch is
m = 2000 - t2 - 140t
where t is measured in minutes. During what time is the mass of fuel greater than 500 Mg?
3. The object distance p, and the image distance q, for a camera of focal length 3 cm is given by:
For what values of q is p > 12 cm?
Didn't find what you are looking for on this page? Try search:
The IntMath Newsletter
Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!
Algebra Lessons on DVD
Easy to understand algebra lessons on DVD. See samples before you commit.
More info: Algebra videos
Book mark this page
Add this page to Del.icio.us, Furl, Digg, StumbleUpon, Google, whatever...
Need a break? Play a math game. Well, they all involve math... No, really!
