Integer solutions to inequalities

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When solving inequalities there will be a range of answers because any numbers represented by the range are acceptable, and there are an amount of solutions to inequalities.

For example, 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 \(-3 \textless 2 e \leq 8\).

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Inequalities - EduqasInteger solutions to inequalities