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A number line is a visual representation of numbers on a straight line. It helps us understand the relative position of numbers.
Positive numbers are placed to the right of zero, and negative numbers are placed to the left. The further right you go, the larger the number becomes. Conversely, the further left you go, the smaller the number.
For example, \( -6 \) is placed six units to the left of zero, while \( -1 \) is placed one unit to the left. This shows us that \( -6 \) is smaller than \( -1 \) because it is further left on the number line.

Inequalities are used to compare two numbers or expressions. They tell us if one value is less than, greater than, or equal to another value.
An inequality can have one of these symbols:

• \( < \) (less than)
• \( > \) (greater than)
• \( \leq \) (less than or equal to)
• \( \geq \) (greater than or equal to)
  
  In our example, \( -6 \leq -1 \) is an inequality. It asks if \( -6 \) is less than or equal to \( -1 \). By comparing their positions on the number line, we see that \( -6 \) is indeed less than \( -1 \), making the inequality true.
  It is essential to look at the context and symbols carefully to understand and solve inequalities correctly.

Comparing negative numbers might seem tricky at first, but using the number line makes it simpler.
Negative numbers are less than zero and are found to the left of zero on a number line. The more negative a number, the smaller its value.
When comparing two negative numbers, the number further to the left is considered smaller. For instance, \( -6 \) is to the left of \( -1 \), so \( -6 \) is smaller than \( -1 \).
This concept also helps us understand inequalities involving negative numbers. In our example, since \( -6 \) is to the left of \( -1 \) on the number line, the statement \( -6 \leq -1 \) is true.
Always remember: as the magnitude of a negative number increases, its value decreases.
This fact is crucial when working with inequalities.