Look at two cases:Mr Davis 97 said:I have the following equation: ##\left | r-5 \right | = \left | r+2 \right |##.
What is a general, analytical way that I can solve equations like these? I always get stumped when trying to solve them...
An absolute value equation is an equation that contains an absolute value expression, which is represented by two vertical bars enclosing a number or expression. The absolute value of a number is its distance from 0 on a number line, and it is always positive.
To solve an absolute value equation, you need to isolate the absolute value expression on one side of the equation and then set up two equations, one with the positive value and one with the negative value of the absolute value expression. Solve both equations and check your solutions to see if they satisfy the original absolute value equation.
Yes, an absolute value equation can have one, two, or no solutions. It depends on the value of the absolute value expression and the other terms in the equation. If the absolute value expression has a coefficient, the equation may have more than two solutions.
Yes, an absolute value equation can be written as a single equation by using the concept of "distance from 0". For example, the absolute value equation |x-2| = 4 can be written as x-2 = 4 or x-2 = -4, which can then be solved for x.
Solving absolute value equations is useful in various mathematical and scientific applications. It can help find the distance between two points on a number line, calculate the magnitude of a vector, or determine the absolute error in a measurement. It is also used in solving real-world problems involving inequalities and absolute value functions.