Questions: x<0 x ≤ -2

Transcript text: 4. $\left.\begin{array}{l}x<0 \\ x \leq-2\end{array}\right)$

Solution

Solution Steps

Step 1: Identify the lines and points on the graph

The graph shows three lines with different slopes and intercepts. The lines intersect at specific points, and some points are marked with open or closed circles.

Step 2: Determine the equations of the lines

The first line passes through the points (-2, 2) and (0, 0). The slope (m) is calculated as: \[ m = \frac{2 - 0}{-2 - 0} = -1 \] The equation of the line is $ y = -x $.
The second line passes through the points (0, 0) and (4, -2). The slope (m) is calculated as: \[ m = \frac{-2 - 0}{4 - 0} = -\frac{1}{2} \] The equation of the line is $ y = -\frac{1}{2}x $.
The third line is horizontal and passes through the point (4, -2). The equation of the line is $ y = -2 $.

Step 3: Identify the regions and inequalities

For the line $ y = -x $:
- Above the line: $ y > -x $
- Below the line: $ y < -x $
For the line $ y = -\frac{1}{2}x $:
- Above the line: $ y > -\frac{1}{2}x $
- Below the line: $ y < -\frac{1}{2}x $
For the line $ y = -2 $:
- Above the line: $ y > -2 $
- Below the line: $ y < -2 $