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Inequalities - OCRInteger solutions to inequalities

Inequalities show the relationship between two expressions that are not equal to one another. Inequalities are useful when projecting profits and breakeven figures. In this OCR Maths study guide, you can revise the more than and less than signs, how to solve inequalities and how inequality can be represented graphically.

Part of MathsAlgebra

Integer solutions to inequalities

If \(a \textgreater 3\), then any number that is bigger than 3 is a possible answer, from any decimal slightly bigger than 3 to infinity.

Sometimes, only solutions are required.

Example

List the integer solutions to \(-5 \textless k \textless 1\).

This can be read as -5 is less than \(k\), which is less than 1.

That means that \(k\) is larger than -5, but not equal to -5, so the smallest integer that \(k\) can be is -4.

\(k\) is less than 1, but not equal to 1, so the largest integer that \(k\) can be is 0.

\(k\) can also be the integers between -4 and 0.

This means that the integer solutions to \(-5 \textless k \textless 1\) are: -4, -3, -2, -1, 0.

Question

List the integer solutions of \(-3 \textless 2 e \leq 8\).