Given the equation square root of 2x+1=3 solve for x and identify if it is an extraneous solution

x=4 and I believe it is an extraneous solution, to see if it is extraneous or not

* put x=4 in the original given equation, to see if it satisfies , if not then the solution is not extraneous.

Given the equation:        ......[1]

Taking square both sides, we get;

Subtract 1 from both sides we get;

2x = 8

Divide both sides by 2 we get;

x = 4

Extraneous solution states that it is a root of a transformed equation that is not a root of the original equation because it was excluded from the domain of the original equation.

Substitute the value of x in [1] we get;

  True.

Therefore, the value of x is 4 and it is not an extraneous solution.