Inequalities

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?

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 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 ».