To determine the solution to the inequality [tex]\(\frac{1}{7} m \leq -\frac{1}{22} \)[/tex], we need to isolate the variable [tex]\( m \)[/tex]. We'll solve the inequality step-by-step.
1. Start with the given inequality:
[tex]\[
\frac{1}{7} m \leq -\frac{1}{22}
\][/tex]
2. To isolate [tex]\( m \)[/tex], multiply both sides of the inequality by 7 (the reciprocal of [tex]\(\frac{1}{7}\)[/tex]):
[tex]\[
7 \cdot \frac{1}{7} m \leq 7 \cdot -\frac{1}{22}
\][/tex]
3. Simplify the left side of the inequality:
[tex]\[
m \leq -\frac{7}{22}
\][/tex]
Now that we have the inequality solved for [tex]\( m \)[/tex], we need to graph the solution on a number line:
1. Identify the critical value, [tex]\(-\frac{7}{22}\)[/tex]:
- First, approximate [tex]\(-\frac{7}{22}\)[/tex]. Since [tex]\(\frac{7}{22}\)[/tex] is approximately 0.318, [tex]\(-\frac{7}{22}\)[/tex] is approximately -0.318.
2. Draw a number line, marking [tex]\(-\frac{7}{22}\)[/tex] at the appropriate point (around -0.318):
3. Since the inequality is [tex]\( \leq \)[/tex], we use a closed circle on [tex]\(-\frac{7}{22}\)[/tex] to indicate that this point is included in the solution set.
4. All values less than or equal to [tex]\(-\frac{7}{22}\)[/tex] satisfy the inequality. Therefore, shade the number line to the left of [tex]\(-\frac{7}{22}\)[/tex].
The resulting graph will have a closed circle on [tex]\(-\frac{7}{22}\)[/tex] (approximately -0.318), and the line to the left of this point will be shaded, representing all values [tex]\( m \leq -\frac{7}{22} \)[/tex].
In summary, the graph representing the solution to the inequality [tex]\(\frac{1}{7} m \leq -\frac{1}{22} \)[/tex] will have a closed circle on [tex]\(-\frac{7}{22}\)[/tex] and shading extending to the left of this point.
