To represent the solution of an inequality on a number line, you'll use dots and shading. For strict inequalities (< or >), use an open dot to show that the endpoint is not included in the solution. For non-strict inequalities (≤ or ≥), use a solid dot to indicate that the endpoint is part of the solution. After marking the endpoint, shade the number line to the left for "less than" inequalities and to the right for "greater than" inequalities. The shaded region represents all the values that satisfy the inequality.

Yes, you can have compound inequalities that combine both "AND" and "OR" conditions, although they might be more complex to solve and interpret. An "AND" condition means both inequalities must be true simultaneously, while an "OR" condition means at least one of the inequalities must be true. When solving such compound inequalities, it's helpful to solve each inequality separately first and then combine the solutions based on the given conditions. Graphically, "AND" conditions often result in a single continuous shaded region on the number line, while "OR" conditions can result in two or more separate shaded regions.

When solving inequalities involving absolute values, it's essential to remember the definition of absolute value: the distance of a number from zero on the number line. For example, to solve |x - 2| > 5, you're looking for values of x that are more than 5 units away from 2. This leads to two inequalities: x - 2 > 5 (which gives x > 7) and x - 2 < -5 (which gives x < -3). So, the solution would be x < -3 or x > 7. Always break down absolute value inequalities into two separate inequalities to solve them.

When you multiply or divide both sides of an inequality by a negative number, the order of the numbers gets reversed. For example, consider the simple fact that 2 is greater than 1. If you multiply both sides by -1, you get -2 and -1. Now, -2 is less than -1, not greater. So, the inequality sign must be reversed to maintain the relationship's truth. Failing to reverse the inequality sign when multiplying or dividing by a negative number can lead to incorrect solutions.

A strict inequality is one that uses the symbols < (less than) or > (greater than). It indicates that one value is strictly less than or strictly greater than another, without being equal to it. For example, x > 3 means that x can be any value greater than 3, but not 3 itself. On the other hand, a non-strict inequality uses the symbols ≤ (less than or equal to) or ≥ (greater than or equal to). It means that one value can be less than, equal to, or greater than another value. For instance, x ≤ 3 means x can be any value less than or equal to 3, including 3 itself.