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Inequalities help us understand how numbers relate to each other. They tell us which number is bigger or smaller. Two main symbols are used in inequalities: '<', which means 'less than', and '>', which means 'greater than'. For example, in the inequality \(3 < 5\), it means that 3 is less than 5. Conversely, \(7 > 2\) means 7 is greater than 2. Understanding these signs is crucial for comparing numbers, especially when dealing with negative numbers. When comparing two numbers, always remember the less-than symbol points to the smaller number, and the greater-than symbol opens to the larger number.

A number line is a visual way to represent numbers. It helps us see the relative positions of numbers. On a number line, numbers increase as you move to the right and decrease as you move to the left.
Let's consider our exercise: comparing \(-12.5\) and \(-9.4\). When we place these numbers on a number line, \(-12.5\) will be to the left of \(-9.4\) because it is smaller. The further left you go, the smaller the number. For positive numbers, the further right you go, the larger the number.
Using a number line can make it easier to visualize and solve inequalities. It becomes clearer which number is bigger or smaller when you see their positions on the line.

Negative numbers can be tricky because they behave differently from positive numbers. They are all less than zero and are found to the left of zero on a number line. The larger the absolute value of a negative number, the smaller its actual value. For instance, while \( -12\) is ‘larger’ than \( -3\) in absolute value, \( -12\) is actually much smaller than \( -3\) because it is further to the left on the number line.
With our exercise, \(-12.5 < -9.4\), we can see this concept in action. Though \(-12.5\) has a larger absolute value than \(-9.4\), it is actually less because it is more negative.
Remembering how negative numbers work will help you correctly apply inequalities and understand their relationships.