- #1
lepton123
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Homework Statement
abs(x+y+z)≤abs(x)+abs(y)+abs(z) indicate when this equality holds and prove this statement
Homework Equations
Triangle inequality?
The Attempt at a Solution
I have nothing :/
Absolute value equality is a mathematical concept that refers to the condition where two quantities have the same absolute value, or magnitude, but may have different signs. In other words, it is the state of being equal in distance from zero on a number line.
In regular equality, two quantities must have the same value in order to be considered equal. However, in absolute value equality, the two quantities must have the same absolute value, regardless of their actual numerical value.
The rules for solving absolute value equations are as follows:1. Isolate the absolute value expression on one side of the equation.2. Set up two separate equations, one with the positive value of the absolute value expression and one with the negative value.3. Solve both equations for the variable.4. Check your solutions by plugging them back into the original equation.
Absolute value equality can be applied in various fields, such as physics, engineering, and economics. For example, in physics, it is used to calculate the distance between two points or the difference between two forces. In engineering, it can be used to determine the tolerance level of a certain measurement. In economics, it can be used to calculate profits and losses.
To graph an absolute value equation, plot the vertex (the point where the absolute value expression equals zero) and another point on either side of the vertex. Then, draw a V-shaped graph connecting the two points. Remember to label the axis and include the absolute value symbol on the graph.