Question

graph the inequality in the coordinate plane.
x < -5

Explanation:

Step1: Analyze the inequality type

The inequality is \( x < - 5 \), which is a linear inequality in one variable, representing a vertical line in the coordinate plane. For the inequality \( x < a \) (where \( a=-5 \) here), the boundary line is \( x = - 5 \), which is a vertical line parallel to the \( y \)-axis passing through \( x=-5 \). Since the inequality is strict (\( < \), not \( \leq \)), the boundary line should be dashed.

Step2: Determine the region to shade

For the inequality \( x < - 5 \), we need to shade the region where the \( x \)-coordinate of the points is less than - 5. So we shade the area to the left of the line \( x=-5 \).

Step3: Graph the boundary line and shade the region

1. Draw the vertical line \( x = - 5 \) as a dashed line (because the inequality is strict, points on the line \( x = - 5 \) do not satisfy \( x < - 5 \)).
2. Shade the region to the left of the line \( x=-5 \) to represent all the points \((x,y)\) where \( x < - 5 \) (the \( y \)-coordinate can be any real number).

Answer:

To graph \( x < - 5 \):

1. Draw a dashed vertical line at \( x=-5 \) (since \( x=-5 \) is not included in the solution set).
2. Shade the region to the left of the line \( x = - 5 \) (this region contains all points with \( x \)-value less than - 5, and any \( y \)-value).