- Addition, subtraction, multiplication, and division;
- Taking opposites, reciprocals, and absolute values;
- Piecewise defined expressions whenever the conditions are given by intervals;
- Raising to powers whenever the base is always positive;
- Raising to powers whenever the exponent is always a whole number;
- Extracting roots whenever the radicand is always positive;
- Extracting roots whenever the index is always a whole number;
- Taking logarithms (as long as they're defined as real numbers);
- Applying any of the trigonometric or inverse trigonometric operations from Chapters 7 and 8 that you might learn about in Trigonometry.

Here is the method:

- Turn the inquality into an equation.
- Solve the equation (this is generally the hard part).
- Also find when the expressions in the original inequality are undefined.
- Finally, find all of the endpoints in the intervals of a piecewise defined function.
- Using the numbers found in the previous two setps, pick one number between each pair of consecutive numbers, as well as one number on either side, as long as the function is defined there.
- For each of the numbers found in the previous steps, check whether the inequality is true or false there.
- The only way for the inequality to shift from true to false is by going through a place where the equation is true or undefined, so now you can read off the answer.

Go back to the course homepage.

This web page was written in 2015 by Toby Bartels, last edited on 2015 December 8. Toby reserves no legal rights to it.

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