Question

If \( \sqrt{3}x - 2 = 2\sqrt{3} + 4 \), then the value of \( x \) is:

• A. \( 1 + \sqrt{3} \)
• B. \( 2(1 + \sqrt{3}) \)
• C. \( 1 - \sqrt{3} \)
• D. \( 2(1 - \sqrt{3}) \)

Hint:

When solving equations with square roots, isolate the term with the square root and simplify carefully. Rationalize the denominator if necessary.

Answer 1

The Correct Option is B

We solve the equation: \[\n\sqrt{3}x - 2 = 2\sqrt{3} + 4\n\] Add 2 to both sides: \[\n\sqrt{3}x = 2\sqrt{3} + 6\n\] Divide both sides by \( \sqrt{3} \): \[\nx = \frac{2\sqrt{3} + 6}{\sqrt{3}} = \frac{2\sqrt{3}}{\sqrt{3}} + \frac{6}{\sqrt{3}} = 2 + \frac{6}{\sqrt{3}}\n\] Simplify \( \frac{6}{\sqrt{3}} \): \[\n\frac{6}{\sqrt{3}} = \frac{6\sqrt{3}}{3} = 2\sqrt{3}\n\] Therefore: \[\nx = 2 + 2\sqrt{3}\n\] Factor out 2: \[\nx = 2(1 + \sqrt{3})\n\] The solution is \( 2(1 + \sqrt{3}) \).