#### Answer

$c=\frac{3}{2}$

#### Work Step by Step

We start with the given equation: $5x=2-(x-7)$
We apply the distributive property to the right side of the equation: $5x=2-x+7$
We add $x$ to both sides of the equation: $5x+x=2+x-x+7$
We combine like terms: $6x=9$
We divide by $6$ on each side of the equation: $$\frac{6x}{6}=\frac{9}{6}$$$$c=\frac{3}{2}$$