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A number line is an essential tool in graphing inequalities and provides a visual representation of numbers laid out in a horizontal line. To depict an inequality on a number line, you start by drawing a straight, horizontal line and marking increments that represent numbers at equal intervals. When working with the inequality like
\( x \text{\geq} -3 \), it is important to clearly plot the point of interest, which in this case is -3.
For students, ensuring clarity in marking and labeling is crucial as it helps to recognize which part of the number line is relevant to the inequality. Moreover, using a straight edge when drawing your number line can greatly improve the neatness and accuracy of your graph.
In summary, the number line serves as the foundation where inequality solutions are visually mapped, and attention to detail can greatly enhance your ability to graph such solutions correctly.

Inequality symbols are the shorthand that mathematicians use to compare relative sizes or order of numbers. The main symbols to note are '<', '<=', '>', and '>='. Understanding these symbols is integral to interpreting and graphing inequalities.
For instance, when you encounter \( x \text{\geq} -3 \), the symbol '>=', or 'greater than or equal to', informs us that x represents all numbers that are -3 or larger. If the symbol was '>' without the equal sign, -3 would not be considered part of the solution set. Similarly, if it was '<' or '<=', we would consider numbers less than -3, with '<=' including -3 itself.
It is also important to note that inequality symbols truly dictate the shading when graphing. The direction they 'point' to helps students visualize the solution set on the number line.

Shading solution regions on a number line is the final step in graphing inequalities, which visually demonstrates where the acceptable solutions lie according to the inequality. The conventional method involves shading or highlighting the portion of the number line that contains all possible solutions.
In the case of \( x \text{\geq} -3 \), you would shade to the right of -3 since the inequality includes numbers that are equal to or greater than -3. A 'closed circle' is drawn at -3 to specify that -3 itself is a valid solution — an important distinction as an 'open circle' would mean -3 is not included.
Subtle as it may seem, proper shading is fundamentally important in illustrating the correct solution set. It is an effective visual cue that helps students verify at a glance whether a particular number is a solution of the given inequality.