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When solving inequalities, the goal is to find the set of values that make the inequality true. It involves similar steps to solving equations but with a few additional rules. Here's how you can approach it:

1. **Rearrange the Inequality**: Start by ensuring the variable (like \(x\)) is isolated on one side of the inequality. For example, given \(5-x \leq 1\), subtract 5 from both sides to get \(-x \leq -4\).

2. **Handling Negative Coefficients**: When multiplying or dividing both sides of an inequality by a negative number, flip the inequality sign. In this case, multiply both sides by -1, which changes \(-x \leq -4\) to \(x \geq 4\).

Understanding these steps helps ensure you find the correct solution while maintaining the relationship expressed by the inequality.

Graphing solutions of inequalities helps visualize the set of possible values. You'll often use a number line for this purpose. Here's how to graph an inequality like \(x \geq 4\):

- **Plot Known Values**: Identify the critical number from your solution, which here is 4. Use a filled-in dot when the variable equals the number (\(x = 4\)).

- **Direction Matters**: Since \(x\) can be any value greater than 4, draw an arrow extending to the right from the dot. This arrow shows that all numbers greater than 4 satisfy the inequality.

By graphing, you gain a clear visual interpretation of the inequality, making it easier to understand the solution set.

A number line offers a straightforward way to represent solutions of inequalities.

1. **Identifying the Key Point**: Start by marking the critical value (in this case, 4) on the number line.

2. **Include or Exclude**: Use a filled dot to indicate that the number is included in the solution (\(x \geq 4\)). If it were \(x > 4\), you'd use an open dot to show that 4 is not included.

3. **Show Direction**: Draw an arrow from the dot to indicate all numbers greater than 4. This visual helps you quickly see the range of solutions.

Using a number line makes interpreting solutions intuitive, providing a quick visual summary of the inequality's range.