Absolute value is a mathematical concept that represents the distance of a number from zero on the number line. It is always positive and is denoted by two vertical lines surrounding the number.
To solve inequalities involving absolute value, you need to isolate the absolute value expression on one side of the inequality and then consider two cases: when the expression inside the absolute value is positive and when it is negative. For each case, you can remove the absolute value by changing it to a positive or negative version of the expression and then solve for the variable.
Absolute value always gives a positive number, while regular value can be positive, negative, or zero. Absolute value also represents distance, while regular value is the actual value of a number.
To graph absolute value inequalities, you first need to rewrite the inequality in the form of y = |ax + b| + c, where a, b, and c are constants. Then, you can plot the vertex at (b, c) and use the slope of a to determine the direction of the graph. Finally, you can shade the appropriate region based on the inequality symbol.
Absolute value and inequalities are used in a variety of fields, such as engineering, physics, and economics. In engineering, they are used to calculate distances and determine the strength of materials. In physics, they are used to describe the motion of objects. In economics, they are used to represent supply and demand, as well as inequalities in income distribution.