To solve the equation √(2x + 1) = 3, we start by eliminating the square root. We can do this by squaring both sides of the equation:
(√(2x + 1))² = 3²
This simplifies to:
2x + 1 = 9
Next, we want to isolate the variable x. We do this by subtracting 1 from both sides:
2x = 9 – 1
2x = 8
Now, we divide both sides by 2:
x = 8 / 2
x = 4
Now we have a potential solution: x = 4. However, we need to check whether this solution is extraneous. An extraneous solution is a solution that does not satisfy the original equation.
We check by substituting x = 4 back into the original equation:
√(2(4) + 1) = √(8 + 1) = √9 = 3
Since both sides of the equation are equal, x = 4 is indeed a valid solution and not an extraneous one.
In summary, the solution to the equation √(2x + 1) = 3 is x = 4, and it is not an extraneous solution.