Inequality basics

Interpret inequalities and check how operations affect their solution relationships.

Meaning

An inequality compares sizes. Adding or subtracting the same number preserves direction; multiplying or dividing by a negative reverses the order. Multiplication by a negative reflects positions across zero and reverses their left-to-right order. For example, 1<3 but −1>−3. The inequality sign must therefore reverse when multiplying or dividing by a negative.

Example

Dividing by -2 gives The original inequality holds at but not at Keeping the sign unchanged when dividing by a negative changes the solution set. Check the multiplier or divisor's sign first.

Practice for this concept

Scope and references

Topics

Inequality signs, properties, reversing order when multiplying or dividing by a negative

Learning goal

Interpret inequalities and check how operations affect their solution relationships.

Helpful background

Connect numerical order with multiplication by a negative.

Basics of inequalities

These ordinary choice questions provide limited practice in this concept. They do not establish independent solution, full-concept performance, or mastery.

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