Question

Two possible solutions of mc003-1.jpg are –7 and 1. Which statement is true?
Only x = –7 is an extraneous solution.
Only x = 1 is an extraneous solution.
Both solutions are extraneous.
Neither solution is extraneous.

Answer 1

I can’t tell from "mc003-1.jpg" because the equation/image wasn’t included. To decide which solution (–7 or 1) is extraneous you need to check each in the original equation (and any domain restrictions). Steps:

1. Substitute x = 1 into the original equation. If it makes a true statement and does not violate any domain restriction (e.g. square-root radicand ≥ 0, denominator ≠ 0), then x = 1 is not extraneous.
2. Substitute x = –7 and do the same check.
3. If a value fails the original equation or violates a domain restriction it is extraneous; otherwise it is a valid solution.

If you paste or upload the equation (or the image), I’ll check both and tell you which statement is true.