Question

Do these 3 and show your work

Answer 1

$Domain:\ x\neq-6\\\\\dfrac{5}{x+6}=10\to\dfrac{5}{x+6}=\dfrac{10}{1}\ \ \ \ |\text{cross multiply}\\\\10(x+6)=(5)(1)\ \ \ \ \ |\text{use distributive property}\\\\(10)(x)+(10)(6)=5\\\\10x+60=5\ \ \ \ |-60\\\\10x=-55\ \ \ \ |:10\\\\\boxed{x=-5.5}\in D$

$Domain:\\\dfrac{5}{x+6}\geq0\ \wedge\ x+6\neq0\to x+6 > 0\to x > -6\\\\\sqrt{\dfrac{5}{x+6}}=10\ \ \ \ \ |^2\\\\\left(\sqrt{\dfrac{5}{x+6}}\right)^2=10^2\\\\\dfrac{5}{x+6}=100\\\\\dfrac{5}{x+6}=\dfrac{100}{1}\ \ \ \ |\text{cross multiply}\\\\100(x+6)=5\ \ \ \ \ |:100\\\\x+6=0.05\ \ \ \ \ |-6\\\\\boxed{x=-5.95}\in D$

$Domain:x+3\geq0\to x\geq-3\\\\\sqrt{2x+3-x}=2\to\sqrt{x+3}=2\ \ \ \ |^2\\\\(\sqrt{x+3})^2=2^2\\\\x+3=4\ \ \ \ |-3\\\\\boxed{x=1}\in D$