Question

Sketch the graph of the inequality. $$x<\frac{1}{2}$$

Short answer

The graph of the inequality is a number line with an open circle at \(\frac{1}{2}\) and shading to the left of this point.

Step-by-step solution

Understand the inequality

The inequality \(x < \frac{1}{2}\) states that the solution includes all \(x\) values that are less than \(\frac{1}{2}\). This does not include \(\frac{1}{2}\) itself since there is no 'or equal to' in the inequality symbol.

Draw a number line

Draw a horizontal line to represent the number line. Mark the point where \(x = \frac{1}{2}\) on the line. If the inequality included \(\frac{1}{2}\) itself (i.e., if it had been \(x \leq \frac{1}{2}\)), we would draw a filled dot at this point. However, because our inequality is strictly less than \(\frac{1}{2}\), we draw an open circle at this point.

Color the solution range

Since \(x\) is less than but not equal to \(\frac{1}{2}\), this means all values of \(x\) to the left of \(\frac{1}{2}\) are included in the solution. To indicate this, we shade or color the portion of the number line to the left of the open circle.