BeginnerTopic 11 of 104Engineering Mathematics
Inequalities
Describe ranges of acceptable values such as tolerances and safety limits.
In depth
Inequalities use <, ≤, > and ≥. Solve like equations, except multiplying or dividing by a negative number reverses the sign. Solutions are intervals. Engineers use them for tolerances, safe operating ranges and constraints in optimisation.
Key points
- Absolute value abs(x-a)<d means a-d<x<a+d
- Test intervals using sign charts
- Strict versus non-strict matters at boundaries
ExampleA shaft of 20±0.05 mm must satisfy 19.95 ≤ d ≤ 20.05.
Engineering requirements are almost always ranges, such as a tolerance band or a safe operating window, and inequalities express them exactly.
What is Inequalities?
Describe ranges of acceptable values such as tolerances and safety limits.
Why is it important to understand inequalities?
Engineering requirements are almost always ranges, such as a tolerance band or a safe operating window, and inequalities express them exactly.
How do I solve an inequality that involves a fraction?
Multiply both sides by the denominator only after checking its sign. If the sign is negative, reverse the inequality.
What is the difference between a strict and a non-strict inequality?
Strict uses less than or greater than and excludes the boundary. Non-strict uses the or-equal forms and includes it, which matters for safety limits.
How is Inequalities used in practice?
Typical applications include writing a tolerance of plus or minus 0.05 mm as an inequality, stating the maximum allowable stress in a code check and defining the acceptable temperature range of a sensor.
What should I learn before Inequalities?
Study "Polynomials and factoring" first (topic 10 of 104 in Engineering Mathematics). It covers the groundwork this topic builds on.
What are the key points of Inequalities?
Absolute value abs(x-a)<d means a-d<x<a+d. Test intervals using sign charts. Strict versus non-strict matters at boundaries.
Can you give an example of Inequalities?
A shaft of 20±0.05 mm must satisfy 19.95 ≤ d ≤ 20.05.
What comes after Inequalities?
The next topic is "Functions and graphs", which builds directly on this one.
How difficult is Inequalities?
It is classed as Beginner in Engineering Mathematics (topic 11 of 104). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.