Absolute value equations

The  exercise appears under the Algebra I Math Mission. This exercise practices solving absolute value and recognizing how these are different from but related to linear equations.

Types of Problems
There is one type of problem in this exercise:


 * 1) Solve the absolute value equation: This problem provides an absolute value equation and asks the student to find all solutions and write them in the space provided.Ave1.png

Strategies
Knowledge of the properties of equality and some experience with absolute value would help when performing this exercise.
 * 1) Absolute value represents distance, so |x-a|=c means the two points that are a distance of c away from a.
 * 2) Once the absolute value is isolated, the absolute value can you be though of under it's distance definition to increase efficiency.
 * 3) Treat the absolute value as a variable, and isolate the absolute value first. Then the absolve value equation can be split into a "positive" equation and a "negative equation."
 * 4) If the absolute value expression is equal to a negative number there is no solution.

Real-life Applications

 * 1) Absolute value can be used in applications connecting algebra to geometry.
 * 2) The absolute value function is an example of a continuous but non-differentiable function (specifically at zero).
 * 3) Absolute value extends into the concept of modulus for complex numbers.