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Understanding inequality notation is crucial when solving and graphing inequalities. Inequalities are expressions that compare two values, such as '<' for less than, '>' for greater than, 'leq' for less than or equal to, and 'greq' for greater than or equal to. These symbols are at the heart of inequality problems, telling us how two quantities relate to each other.

For example, the inequality 'x greq 3' means that the variable 'x' can take any value that is either 3 or greater than 3. It's essential to treat the inequality sign as a guide that directs which numbers are part of the solution set. In our exercise, since we are dealing with 'greq', we know that 3 is a part of the solution, and so is every number greater than 3. This understanding is the first step in approaching inequalities, making it easier to solve and represent them accurately.

A number line is a visual tool that helps to represent and comprehend mathematical concepts such as inequalities. To represent an inequality on a number line, one should first draw a horizontal line divided into equal intervals and mark numbers accordingly.

h4 Representation Rules When representing an inequality, use a filled circle or dot to denote included values, like the number 3 in the inequality 'x greq 3'. Conversely, an open circle indicates that a value is not included. In the present case, since 3 is included (the 'equal to' part of 'greq'), we depicted it with a filled dot on the number line. The area representing all the numbers that satisfy the inequality is typically shown by shading or darkening the line. For 'x greq 3', the line is darkened to the right of the 3, continuing infinitely, to show all numbers greater than or equal to 3.

Solving inequalities is a systematic process that involves finding all possible solutions that satisfy the given inequality. To solve an inequality like 'x greq 3', begin by isolating the variable—though in this straightforward case, the variable 'x' is already isolated.

The solution set includes all numbers that make the inequality true. In practice, you test various numbers to confirm if they work; for example, inserting 2 does not satisfy the inequality since 2 is less than 3, but inserting 4 does, because 4 is greater than 3.

The final solution set is expressed in interval notation, for instance, '[3, ingty)'. This reads as 'all numbers from 3 to infinity', where '3' is included, denoted by the square bracket, and infinity is always accompanied by a parenthesis since it is not a real number and can't be 'reached'. Remember, inequality solving not only involves finding the solution but also representing it correctly whether it be in set, interval, or graphical form on a number line.