Step-by-step explanation:
[tex] {2}^{(x + 2)} + \frac{ {2}^{(x + 3)} }{2} = 1 \\ \\ \therefore \: {2}^{(x + 2)} + \frac{ {2}^{(x + 2 + 1)} }{2} = 1 \\ \\ \therefore \: {2}^{(x + 2)} + \frac{ {2}^{(x + 2 )} \times {2}^{1} }{2} = 1 \\ \\ \therefore \: {2}^{(x + 2)} + \frac{ {2}^{(x + 2 )} \times {2} }{2} = 1 \\ \\ \therefore \: {2}^{(x + 2)} + {2}^{(x + 2 )} = 1 \\ \\ \therefore \: 2 \times {2}^{(x + 2)} = {2}^{0} \: ( \because \: {a}^{0} = 1) \\ \\ \therefore \: {2}^{(x + 3)} = {2}^{0} \\ \\ \therefore \: x + 3 = 0 \\ \\ \huge \red{ \boxed{\therefore \: x = - 3}}[/tex]
