How do you solve \[\dfrac{1}{4}m \leqslant - 17\]?

Hint: The given question is a linear inequation. So, we will not get a single value for the variable, instead we will get a range of values for the variable. To solve this, we will cross-multiply the denominator to the RHS and then write the value of \[m\], then we will also show it on the number line.

Complete step by step answer:
The given question is:
\[\dfrac{1}{4}m \leqslant - 17\]
Now we will cross multiply the denominator to the RHS. So, we have;
\[ \Rightarrow m \leqslant - 17 \times 4\]
On multiplication we get;
\[ \Rightarrow m \leqslant - 68\]
Now we will represent it on the number line. So, we have;

We can see that if \[m \leqslant - 68\], then it will belong to region1. So,
\[ \Rightarrow m \in ( - \infty , - 68]\]

Note:
One thing to note is that in the case of linear inequation if we multiply both sides by any negative number, then the inequality sign changes. For example, one is less than two but minus one is greater than minus two. Also, if we take the reciprocal then the inequality sign gets reversed. For example, three is greater than two but one by three is less than one by two. Another point to note is the use of brackets. In the given question, since there is equality sign, we have included \[ - 68\] also in our answer and that’s why we have used the square bracket because square brackets include the terminal points also. If the inequality sign is not there, then we simply use the parentheses. Another most important point is we always put parentheses for the infinity sign because we can never include infinity as its exact value is not defined.