91Ó°ÊÓ

Graphing inequalities involves representing a range of solutions on the number line. For an inequality such as \( x \geq -1 \), the goal is to display all values of \( x \) that satisfy this condition. The inequality sign indicates the relationship between \( x \) and a set number, in this case, \(-1\). Since the inequality symbol \( \geq \) includes the equal part, \( x \) can be exactly \(-1\) or any number greater than \(-1\).
Understanding these symbols is crucial:

• \( > \): Greater than
• \( < \): Less than
• \( \geq \): Greater than or equal to
• \( \leq \): Less than or equal to

Each sign tells us how to graphically display the data on a number line, as well as how to interpret the shaded regions and circles associated with it.

Using a number line to represent inequalities helps visualize which values of the variable satisfy the inequality.
To graph \( x \geq -1 \), you first find and mark the number on the line, highlighting the point \(-1\) as the boundary.
This point is drawn on the number line as a solid circle since the inequality includes \(-1\). If the inequality was \( x > -1 \), an open circle would be used instead to show \(-1\) is not part of the solution set.
Next, you shade the line to the right of \(-1\). This visualizes all values greater than \(-1\), continuing towards positive infinity. Shading is an essential way of expressing possible solutions graphically.

The solution set represents all possible values that satisfy the inequality. It’s essential to know what the solution set looks like on a number line.
For \( x \geq -1 \), the solution set includes the point \(-1\) and stretches to every number greater than \(-1\). Writing this mathematically, you express the solution set as:
\[ x \in [-1, \infty) \]The bracket \([\ ]\) around \(-1\) signifies that \(-1\) is included in the solution set, while the parenthesis \((\ ])\) around infinity indicates that while values stretch indefinitely, infinity itself is not a number we reach or include.
In summary, the solution set is easily readable on the number line and can also be represented in interval notation, providing a complete picture of where \( x \) lies.