An absolute value equation describes distance from , so a positive distance can come from either sign inside the bars. If the question asks for a negative solution, that describes , not necessarily the expression inside the bars. For a one-variable equation, use a Desmos regression restricted to negative inputs, then read the value under PARAMETERS.
Hints
- Hint 1
An absolute value is distance from : both and are units away. The negative solution means a negative value of which quantity: or ?
- Hint 2
In a Desmos regression, use for the unknown and to ask Desmos to find its value. Add so it finds the requested negative input.
Step-by-step
Restrict a Desmos regression
Step 1Separate the sign inside the bars from the sign of the solution
The absolute value of a number is its distance from . Both and have absolute value , so the expression inside the bars could satisfy . The negative solution is a negative value of , not necessarily a negative value inside the bars.
- Step 2
Find the negative value of
Type into Desmos. In this regression, is the unknown, tells Desmos to find a value that makes the sides equal, and keeps only a negative input. Under PARAMETERS, Desmos shows . So the negative solution is . Choice C.