Math Lesson 10.1.2 - Solving an Inequality

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Welcome to our Math lesson on Solving an Inequality, this is the second lesson of our suite of math lessons covering the topic of Solving Linear Inequalities, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Solving an Inequality (with one variable)

Solving an inequality means finding the set of values that make the inequality true. This means that when solving an inequality, we don't have to find a finite number of values as solutions, as usually happens in equations, but a set of infinite values instead.

For example, if after doing all necessary operations we obtain x > 3 as the final (simplest) version of inequality, this means all values of the variable x that are greater than 3 are solutions of the given inequality. We say all these values belong to the solution set of that inequality.

Example 1

Which of the following numbers do not belong to the solution set of the inequality

1. 8
2. 7
3. 6
4. 5

Solution 1

1. The number 8 belongs to the solution set of the inequality x ≥ 7 as if we write 8 ≥ 7, this inequality becomes true.
2. The number 7 belongs to the solution set of the inequality x ≥ 7 as if we write 7 ≥ 7, this inequality becomes true.
3. The number 6 does not belong to the solution set of the inequality x ≥ 7 as if we write 6 ≥ 7, this inequality becomes false.
4. The number 5 does not belong to the solution set of the inequality x ≥ 7 as if we write 5 ≥ 7, this inequality becomes false.

More Solving Linear Inequalities Lessons and Learning Resources

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Enjoy the "Solving an Inequality" math lesson? People who liked the "Solving Linear Inequalities lesson found the following resources useful:

1. Solving Feedback. Helps other - Leave a rating for this solving (see below)
2. Inequalities Math tutorial: Solving Linear Inequalities. Read the Solving Linear Inequalities math tutorial and build your math knowledge of Inequalities
3. Inequalities Video tutorial: Solving Linear Inequalities. Watch or listen to the Solving Linear Inequalities video tutorial, a useful way to help you revise when travelling to and from school/college
4. Inequalities Revision Notes: Solving Linear Inequalities. Print the notes so you can revise the key points covered in the math tutorial for Solving Linear Inequalities
5. Inequalities Practice Questions: Solving Linear Inequalities. Test and improve your knowledge of Solving Linear Inequalities with example questins and answers
6. Check your calculations for Inequalities questions with our excellent Inequalities calculators which contain full equations and calculations clearly displayed line by line. See the Inequalities Calculators by iCalculator™ below.
7. Continuing learning inequalities - read our next math tutorial: Quadratic Inequalities

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Inequalities Calculators by iCalculator™

• Quadratic Inequalities Calculator