* Number line of inequality: a) \( x>-3 \)

To represent the inequality \( x > -3 \) on a number line, follow these steps: 1. **Identify the critical point**: The critical point here is \( -3 \). This is the value where the inequality changes. 2. **Determine the type of inequality**: Since the inequality is \( x > -3 \), it means that \( x \) can take any value greater than \( -3 \) but not equal to \( -3 \). 3. **Draw the number line**: - Draw a horizontal line and mark several points on it, including \( -3 \). - Use an open circle at \( -3 \) to indicate that this point is not included in the solution (since \( x \) cannot equal \( -3 \)). - Shade the line to the right of \( -3 \) to indicate that all values greater than \( -3 \) are included in the solution. The representation on the number line would look like this: ``` <---|---|---|---|---|---|---|---|---|---|---> -5 -4 -3 -2 -1 0 1 2 3 4 (-----------------> ``` In this diagram: - The open circle at \( -3 \) indicates that \( -3 \) is not included. - The arrow to the right shows that all values greater than \( -3 \) are part of the solution.