Solve each equation and verify your solution(s). Identify any extraneous roots. 2√6 + 5𝑥 − 2 = 3𝑥

Answer 1

To solve the equation, we first need to combine like terms. We have:

2√6 + 5𝑥 − 2 = 3𝑥

Next, let's subtract 5𝑥 from both sides to isolate the 𝑥 term:

2√6 - 2 = 3𝑥 - 5𝑥

Combining like terms:

2√6 - 2 = -2𝑥

Now, let's divide both sides by -2 to solve for 𝑥:

(2√6 - 2) / -2 = -2𝑥 / -2

Simplifying:

-√6 + 1 = 𝑥

So the solution to the equation is 𝑥 = -√6 + 1.

To verify this solution, substitute 𝑥 = -√6 + 1 back into the original equation:

2√6 + 5(-√6 + 1) - 2 = 3(-√6 + 1)

Simplifying:

2√6 - 5√6 + 5 - 2 = -3√6 + 3

-3√6 + 3 = -3√6 + 3

The equation is verified. There are no extraneous roots in this case.