We want to get rid of the square root sign somehow, so let's isolate that term.
[tex]2\sqrt{\frac{3x}{5}} + 3 = 11[/tex]
[tex]2\sqrt{\frac{3x}{5}} = 11 - 3 = 8[/tex]
[tex]\sqrt{\frac{3x}{5}} = 4[/tex]
Now, in order to 'undo' a root sign, we need to do the opposite to it, by squaring the term, but in order for it to remain the same, we need to square 4 as well.
[tex]\frac{3x}{5} = 16[/tex]
Now, we can isolate the variable:
[tex]3x = 5 \cdot 16 = 80[/tex]
[tex]x = \frac{80}{3}[/tex], and since we can't simplify this further, our final answer becomes:
[tex]x = \frac{80}{3}[/tex] or [tex]x = 26\frac{2}{3}[/tex]
