To graph the inequality [tex]\(a \leq -50\)[/tex], follow these steps:
1. Draw a number line: Begin by drawing a horizontal line and marking it with numbers. Focus on the key number of the inequality, which is [tex]\(-50\)[/tex].
2. Plot the key number: Locate [tex]\(-50\)[/tex] on the number line. Mark this point clearly. Since the inequality is [tex]\(\leq -50\)[/tex], we will indicate that [tex]\(-50\)[/tex] is included in the solution set.
3. Shade the region: For the inequality [tex]\(a \leq -50\)[/tex], we need to identify all the numbers that are less than or equal to [tex]\(-50\)[/tex]. Shade the number line to the left of [tex]\(-50\)[/tex] to represent all numbers smaller than or equal to [tex]\(-50\)[/tex].
4. Use proper notation: Since [tex]\(-50\)[/tex] is part of the solution (the inequality includes [tex]\(-50\)[/tex]), place a solid dot at [tex]\(-50\)[/tex].
The correctly drawn graph for the inequality [tex]\(a \leq -50\)[/tex] will consist of:
- A number line with a solid dot at [tex]\(-50\)[/tex].
- A shaded region extending to the left from [tex]\(-50\)[/tex] and continuing infinitely.
In summary, the graph matches the inequality [tex]\(a \leq -50\)[/tex] by illustrating a solid dot at [tex]\(-50\)[/tex] and shading all values to the left of [tex]\(-50\)[/tex], indicating that all these values are part of the solution set.
