Question

Question 1 (Multiple Choice Worth 5 points)

(01.03 MC)
Given the equation √√3x-2=4, solve for x and identify if it is an extraneous solution.
O 6; solution is extraneous
O 6; solution is not extraneous
O
3
; solution is extraneous
solution is not extraneous

Answer 1

To solve the equation √√3x-2=4, square both sides to eliminate the square root, simplify, isolate x, and check if the solution is extraneous.

Step-by-step explanation:

To solve the equation √√3x-2=4, we need to apply inverse operations to isolate the variable x. Start by squaring both sides of the equation to remove the square root: (√√3x-2)^2 = 4^2. This simplifies to 3x-2 = 16. Next, add 2 to both sides to isolate x: 3x = 18. Finally, divide both sides by 3 to solve for x: x = 6.

Now, we need to check if this solution is extraneous, meaning it does not satisfy the original equation. Substitute x = 6 back into the original equation: √√3(6)-2=4. Simplifying, we get √√18 - 2 = 4. √√18 is approximately 2.633, and 2.633 - 2 = 0.633. Therefore, the left side of the equation does not equal 4, so the solution x = 6 is extraneous.

Learn more about Solving equations involving square roots