DrunkenPhD said:If this is true how to proof
Regards
pwsnafu said:What have you tried?
DrunkenPhD said:Wonder if this is true or just mistype:
|x+y| [itex]\leq[/itex] |x| +|y|
If this is true how to proof because cannot find it out anywhere written
Regards
Inequality with absolute values is a mathematical concept that deals with comparing two numbers or expressions that have absolute values, meaning they are always positive. Inequality with absolute values is often used to represent the distance between two numbers on a number line.
To solve an inequality with absolute values, you first isolate the absolute value expression on one side of the inequality. Then, you can rewrite the absolute value expression as two separate inequalities, one with a positive sign and one with a negative sign. Finally, solve each inequality separately to find the solution set.
The main difference between solving an inequality with absolute values and solving a regular inequality is that when dealing with absolute values, you must consider both the positive and negative values of the expression. This is because the absolute value of a number can be either positive or negative, depending on the value of the number itself.
Yes, you can graph an inequality with absolute values. The graph will show all the values that satisfy the inequality. To graph an inequality with absolute values, you can first graph the two separate inequalities that result from rewriting the absolute value expression, and then find the overlapping region between the two graphs.
Inequalities with absolute values are commonly used in data analysis, economics, and engineering. For example, in economics, absolute value inequalities can be used to represent the relationship between supply and demand. In engineering, they can be used to represent the tolerance of a manufactured part. They can also be used to model real-life situations that involve distance, such as calculating the maximum distance a car can travel on a given amount of gas.