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When it comes to understanding inequalities, one of the best visual tools at our disposal is an inequality graph. What's important in graphing an inequality is knowing that it illustrates a range of solutions. Unlike an equation, where we may have a single answer, an inequality tells us that there may be many acceptable answers.

For example, if you're asked to graph the solution to the inequality from our exercise, you'll need to represent all the values of 'x' that make it true. Since we found that the solutions are all values of 'x' greater than -1.25, it's represented by a number line with a hollow circle at -1.25 – indicating that this number isn't included – and an arrow pointing to the right, signaling that all numbers beyond this point are a part of the solution set.

At the heart of solving inequalities lies the process of algebraic manipulation. This can involve a variety of steps such as distributing multiplication over addition and subtraction, moving terms across the 'inequality sign' by adding or subtracting, and dividing or multiplying both sides by a number. However, there's a key difference in manipulation when it comes to inequalities: if you multiply or divide by a negative number, the inequality sign must be flipped.

In our exercise, we distributed, rearranged terms, and isolated 'x' without flipping the inequality because we divided by a positive number. The goal is to transform the inequality into a simpler form without changing the set of solutions, and the step-by-step solution shows us how to do that effectively.

The number line representation is an extension of graphing the inequality and provides a simple, yet powerful way to visualize the solutions. It's more than just a line; it's a map of where the values lie in relation to one another.

For our exercise, the representation starts with a number line, typically a horizontal line with marks at regular intervals. We drew a hollow circle at -1.25 to show where this boundary is, but we didn't include this number in the set of solutions. From there, the arrow to the right indicates all the numbers greater than -1.25. It's important to note that with a less than (<) inequality, the arrow would have pointed to the left. The number line is a fundamental tool in expressing the infinite nature of our solutions: it carries on indefinitely, but the solutions are clearly shown in one direction.