Algebra and Trigonometry, 5th Edition

1.6 Solving Linear Inequalities

• Solve linear inequalities.

• Solve compound inequalities.

• Solve applied problems using inequalities.

An inequality is a sentence with $<,>,\le$, or$\ge$ as its verb. An example is $3x-5<6-2x$. To solve an inequality is to find all values of the variable that make the inequality true. Each of these values is a solution of the inequality, and the set of all such solutions is its solution set. Inequalities that have the same solution set are called equivalent inequalities.

Linear Inequalities

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The principles for solving inequalities are similar to those for solving equations.

Principles for Solving Inequalities

For any real numbers a, b, and c:

The Addition Principle for Inequalities:

If $a<b$ is true, then ...