An absolute value equation with a positive number on one side can have two solutions: the expression inside the bars can be positive or negative. If the question asks for one possible value, you only need one solution. A Desmos regression can find it, but don't mistake the number outside the bars for the variable's value.
Hints
- Hint 1
An absolute value is a distance from . Both and are units from . What two values could the expression inside the bars have?
- Hint 2
The question asks for one value, and every answer choice is positive. In a Desmos regression, replace with and restrict so Desmos finds a positive solution.
Step-by-step
Use the two-case idea, then Desmos
Step 1Identify what can be inside the bars
An absolute value gives distance from . Since that distance is , the inside can be or : . The inside expression, not by itself, equals one of those numbers.
- Step 2
Find one positive solution
Every answer choice is positive, so ask Desmos for a positive solution. Replace with and type . The tells Desmos to find a value that makes the sides equal; the braces restrict that value to positive numbers. Under PARAMETERS, Desmos shows . So is one possible value. Choice A.