An absolute value equation can have more than one solution because opposite numbers have the same absolute value. If the question asks for a negative solution, apply that condition to the unknown, not automatically to the expression inside the bars. In Desmos, use a regression restricted to negative values to find the solution the question requests.
Hints
- Hint 1
Absolute value measures distance from : a positive number and its negative have the same absolute value. Does negative describe the solution , or does it describe the expression inside the bars?
- Hint 2
If , subtracting makes positive. Restrict when you enter the equation as a regression in Desmos, so it finds the negative solution.
Step-by-step
Restrict the Desmos solve to negative values
Step 1Identify what must be negative
The absolute value bars turn a number into its distance from . If , then , so and . Negative doesn't mean the expression inside the bars is negative.
- Step 2
Find the negative solution
Type in Desmos. Use and to tell Desmos to solve the equation; the braces keep only negative values of . Under PARAMETERS, Desmos shows . So the negative solution is . Choice C.