By M. Bourne
This chapter explains the properties of inequalities and then goes on to show how to solve linear and non-linear inequalities. Finally, we see how to solve inequalities that involve absolute values.
Why study inequalities?
Logo of Devon & Exeter
Racial Equality Council, England
All men are born equal,
but some are more equal
(The root of all prejudice)
Inequalities are very common in daily life. For example:
- Thermostats in cars cause a valve to open when the engine gets hot (say more than `95°"C"`), allowing water to circulate and cool the engine down. We can express this condition using an inequality: `T > 95°"C"`. If the engine is getting too cool (say `T < 85°"C"`), the thermostat closes again, reducing the water circulation.
- A voltage regulator in a TV will typically accept a voltage range from 110V to 240V. We could write the range for the voltage V as `110 ≤ V ≤ 240`.
- Obesity is usually defined in terms of the Body Mass Index (BMI).
- `"BMI" < 18.5` is underweight
- `18.5 < "BMI" < 24.9` is normal weight
- `25.0 < "BMI" < 29.9` is overweight
- `30.0 < "BMI" < 39.9` is obese
- `"BMI" > 40.0` is severely (or morbidly) obese
[The BMI is the mass of the person in kg divided by the square of the person's height in m.]
In this Chapter
- 1. Properties of Inequalities - the difference between "`<`", "`>`", "`≤`" , etc.
- 2. Solving Linear Inequalities - problems like: `3 - 2x ≥ 15`
- 3. Solving Non-Linear Inequalties - more advanced examples
- 4. Inequalities Involving Absolute Values - with examples
Let's first learn some of the Properties of Inequalities ».
Didn't find what you are looking for on this page? Try search:
Online Algebra Solver
This algebra solver can solve a wide range of math problems. (Please be patient while it loads.)
Go to: Online algebra solver
Ready for a break?
Play a math game.
(Well, not really a math game, but each game was made using math...)
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!
Short URL for this Page
Save typing! You can use this URL to reach this page:
Algebra Lessons on DVD
Easy to understand algebra lessons on DVD. See samples before you commit.
More info: Algebra videos