Problem 10 - Algebra and Trigonometry

Question

Graph each inequality. $$x \leq-3$$

Step-by-Step Solution

Answer

The graph of the inequality \(x \leq -3\) is a number line with a closed circle at -3 and shading to the left towards the lesser values. This shaded region represents all possible values of 'x' satisfying the given inequality.

Step 1: Identify the Included Value

Looking at the inequality \(x \leq-3\), the value '-3' is included in the solution since there is an 'or equal to' (\(\leq\)) sign. Hence, -3 is part of the solutions for this inequality.

Step 2: Draw the Number Line

Draw a line, mark it as the number line, and put an arrowhead at both ends to represent the continuation of numbers. Also, put a point or circle on -3 and mark it as x. This point represents the value for x in the inequality.

Step 3: Identify and Shade the Solution Region

Since the inequality is \(x \leq -3\), this means 'x' can be any number less than or equal to -3. Therefore, shade along the line to the left towards the lesser values.