Assessment and Learning in Knowledge Spaces (ALEKS) Basic Math Placement Practice Test

How do you determine the missing variable in an absolute value equation?

1. Test values until you find one that works

2. Set the equation equal to both the positive and negative values

3. Use the quadratic formula

4. Only consider the positive value

The correct answer is: Set the equation equal to both the positive and negative values

To determine the missing variable in an absolute value equation, the correct approach involves setting the equation equal to both the positive and negative values of the expression inside the absolute value. This is because the absolute value function measures the distance of a number from zero on the number line without regard to direction, which means it can yield two possible outcomes: one for the positive scenario and one for the negative. For example, if you have the equation |x| = a, where 'a' is a positive number, this would translate into two separate equations: x = a and x = -a. Solving these equations will give you the necessary values of 'x' that satisfy the original absolute value equation. Testing values until one works is not systematic and could lead to oversight of potential solutions. The quadratic formula is specifically for solving quadratic equations and does not apply here. Considering only the positive value ignores the critical nature of absolute value, which necessitates accounting for both possibilities. Therefore, setting the equation equal to both the positive and negative values is the method that captures all potential solutions accurately.