Question 558195
<pre>
2x=&#8730;(1-3x)
<font color = blue><font size = 2><font face = tahoma><b>***************
The other person's solutions, {{{matrix(1,3, - 1, or, - 1/4)}}} are WRONG!!

{{{2x = sqrt(1 - 3x)}}}
For the RADICAND, 1 - 3x, we have: {{{system(1 - 3x >= 0, - 3x >= - 1, highlight(x <= 1/3))}}}
So, we get: {{{2x = sqrt(1 - 3x)}}}, with {{{highlight(x <= 1/3)}}}
     {{{4x^2 + 3x - 1 = 0}}} <==== Up to this point is CORRECT!
(x + 1)(4x - 1) = 0
                x + 1 = 0    OR    4x - 1 = 0
                      {{{matrix(1,3, x = - 1, or, x = 1/4)}}}
Although both solutions {{{are <= 1/3}}}, x = - 1 is EXTRANEOUS, and so, ONLY VALID/ACCEPTABLE solution is: {{{highlight(x = 1/4)}}}</font></font></font></b></pre>