$\text{a)}f\left(x\right)=\frac{5x+2}{7}$  

$\frac{5x+2}{7}=0\mid \cdot 7$  

$5x+2=0$  

$5x=-2\mid :5$  

$x=-\frac{2}{5}$  

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$\text{b)}f\left(x\right)=\sqrt{4x+1}\text{Zał.}x\ge -\frac{1}{4}$  

$\sqrt{4x+1}=0\mid {}^2$  

$4x+1=0$  

$4x=-1\mid :4$  

$x=-\frac{1}{4}$  

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$\text{c)}f\left(x\right)=\left|x\right|-6$  

$\left|x\right|-6=0$  

$\left|x\right|=6$  

$x=6\text{lub}x=-6$  

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$\text{d)}f\left(x\right)=\frac{3-4x}{5}$  

$\frac{3-4x}{5}=0\mid \cdot 5$  

$3-4x=0$  

$-4x=-3\mid :\left(-4\right)$  

$x=\frac{3}{4}$  

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$\text{e)}f\left(x\right)=\sqrt{2x-6}\text{Zał.}2x-6\ge 0,\text{czyli}x\ge 3$  

$\sqrt{2x-6}=0\mid {}^2$  

$2x-6=0$  

$2x=6\mid :2$  

$x=3$  

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$\text{f)}f\left(x\right)=8-\left|x\right|$  

$8-\left|x\right|=0$  

$\left|x\right|=8$  

$x=8\text{lub}x=-8$