$a\text{)}\sqrt{2}x+3=5\mid -3$  

$\sqrt{2}x=2\mid \sqrt{2}$  

$x=\frac{2}{\sqrt{2}}$     

$x=\frac{2\sqrt{2}}{2}$  

$x=\sqrt{2}$  

---

$b\text{)}\sqrt{5}x-7=3\mid +7$  

$\sqrt{5}x=10\mid \sqrt{5}$  

$x=\frac{10}{\sqrt{5}}$  

$x=\frac{10\sqrt{5}}{5}$  

$x=\sqrt{5}$  

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$c\text{)}2\sqrt{3}x+6=15-7\sqrt{3}x\mid +7\sqrt{3}x$  

$9\sqrt{3}x+6=15\mid -6$  

$9\sqrt{3}x=9\mid :9$  

$\sqrt{3}x=1\mid :\sqrt{3}$  

$x=\frac{1}{\sqrt{3}}$  

$x=\frac{\sqrt{3}}{3}$  

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$d\text{)}1-\sqrt{7}x=\frac{1}{3}\left(12\sqrt{7}x+18\right)\mid \cdot 3$  

$3-3\sqrt{7}x=12\sqrt{7}x+18\mid -12\sqrt{7}x$  

$-15\sqrt{7}x+3=18\mid -3$  

$-15\sqrt{7}x=15\mid :\left(-15\sqrt{7}\right)$  

$x=-\frac{1}{\sqrt{7}}$  

$x=-\frac{\sqrt{7}}{7}$