Question

Given the equation Square root of 2x plus 1 = 3, solve for x and identify if it is an extraneous solution.

Answer 1

$\sqrt{2x+1}=3\\\\The\ domain:\\2x+1\geq0\to x\geq-0.5\\\\D:x\in[-0.5;\ \infty)$

$\sqrt{2x+1}=3\ \ \ \ |square\ both\ sides\\\\2x+1=3^2\\\\2x+1=9\ \ \ \ |subtract\ 1\ from\ both\ sides\\\\2x=8\ \ \ \ |divide\ both\ sides\ by\ 2\\\\x=4\in D\\\\Answer:\boxed{x=4}$