An absolute value is a distance from zero. If it equals a positive number, the expression inside the bars can be either positive or negative. Desmos can find a solution to the equation with a regression; restrict it to one sign when there are two possible solutions. Keep both signs of the inside in mind.
Hints
- Hint 1
Absolute value removes a minus sign: both and have an absolute value of . What two values could the expression inside the bars equal?
- Hint 2
A Desmos regression finds a value of that makes an equation work. To find the negative-inside case, restrict the search to values where .
Step-by-step
Find one solution with a restricted regression
Step 1Account for both signs inside the bars
Absolute value is distance from zero. The given distance is , so the expression inside the bars has two possibilities:
Solving only the positive-inside case could miss a solution.
- Step 2
Find a solution from the negative-inside case
Type in Desmos. Change to and to so Desmos solves for a value instead of graphing the equation. The condition keeps the inside negative, selecting that case. Under PARAMETERS, Desmos shows . So is a solution to the original equation. Choice B.