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The solution set of an inequality like \(4x < 20\) includes all the possible values of \(x\) that make the inequality true.
In mathematical terms, in the solution set, you're looking for all the numbers that fit the condition given by the inequality.
When dealing with \(4x < 20\), the primary task is to solve for \(x\). By dividing both sides by \(4\), we find that \(x < 5\).
This indicates that every number less than \(5\) is a solution to the inequality. To visualize, if you pick any number like \(4, 3.5,\) or even \(-2\), and substitute it back into the original inequality, the inequality holds true.
On the other hand, if you chose a number like \(6\), it wouldn’t fit because \(4 \times 6 = 24\), which is greater than \(20\).
The set of these numbers is what we call the solution set.

Graphing inequalities means representing the range of possible solutions graphically, often on a number line. This visual representation helps in understanding which numbers belong to the solution set.
For the inequality \(x < 5\), the number line graphically signifies all numbers less than \(5\). This involves marking the point \(5\) but not including it in the solution.To show that \(5\) is not part of the solution, an open circle or dot is used at \(5\).
Then a line or ray is drawn extending to the left from the point \(5\), indicating all numbers to the left are part of the solution. This method is straightforward and clearly indicates the solution's boundary.When graphing inequalities:

• An open circle is used for \(<\) or \(>\).
• A closed circle is used for \(\leq\) or \(\geq\) to show inclusion of the boundary value.

This rule of thumb helps quickly differentiate between inclusive and exclusive bounds.

A number line is a visual tool used to represent numbers in a sequential order.
It makes reasoning about numbers and their relationships easier.For example, it can help us see that \(2\) is less than \(5\) since \(2\) is located to the left of \(5\) on the line. In solving inequalities, the number line is essential because it provides a convenient way to display which numbers satisfy the equation.
To place the solution \(x < 5\) on a number line:

• First, identify and mark the number \(5\) on the line.
• Use an open circle at this point to indicate it's not included.
• Draw a ray or arrow extending to the left to signify all numbers less than \(5\).

This representation on a number line offers a clear and understandable approach for visualizing the solutions to inequalities, especially for those new to the concept.