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When working with inequalities like \( -2 \leq x \leq 0 \), it’s important to express the solution set in a concise way. This is where interval notation comes in. In interval notation, square brackets \([ ]\) are used to indicate that an endpoint is included in the interval. This is also known as an 'inclusive' range.
For instance, when we say \([-2, 0]\), we are specifying that all numbers from -2 to 0, including both -2 and 0 themselves, are part of the solution set. This notation is incredibly useful in mathematics because it provides a quick overview of which numbers are included in the range.

• Use \([ ]\) when endpoints are included (like \([-2, 0]\)).
• Use \(( )\) for exclusive ranges, when endpoints are not included.

Understanding this simple yet powerful notation helps in clearly defining the set of numbers that satisfy the inequality.

A number line can be a helpful visual tool when dealing with inequalities. It provides a graphical representation of the solution. For the inequality \(-2 \leq x \leq 0\), drawing a number line involves several steps:

• First, draw a straight horizontal line and position key numbers on it, such as -2 and 0.
• Since the endpoints \(-2\) and \(0\) are included in the solution, place solid dots at these values on the number line.
• Shade the region between -2 and 0 to show all possible solutions for \(x\).

A number line is a simple yet effective way to visually communicate which numbers fulfill the inequality. This helps to solidify the understanding by seeing the continuous range that \(x\) can take.

Solving inequalities and representing their solutions requires understanding what it means for a number to satisfy a given condition. An inequality like \(-2 \leq x \leq 0\) tells us that \(x\) must lie within a certain range. This means:

• \(x\) can take any value that is greater than or equal to \(-2\).
• At the same time, \(x\) must also be less than or equal to \(0\).

This makes the set of solutions a continuous range from \(-2\) to \(0\), inclusive. To find solutions to an inequality, determine these limits and check whether the endpoints are included, typically denoted by 'greater than or equal to' (\(\leq\)) or 'less than or equal to' (\(\geq\)). Understanding these concepts helps you determine all possible values of \(x\) that satisfy the inequality. This forms the basis for correctly graphing on a number line or expressing findings in interval notation.