Answer:
x=2 is our solution
Step-by-step explanation:
Given options:
x = −2
x = −1
x = 1
x = 2
Lets plug in each option and check with the given equation
\(\frac{2}{3} x+\frac{8}{3} =2^x\)
Let plug in each option and check
(A) x=-2, plug in -2 for x
\(\frac{2}{3}(-2)+\frac{8}{3} = 2^{-2}\)
\(\frac{-4+8}{3} =\frac{1}{2^2}\)
\(\frac{4}{3} =\frac{1}{4}\)
It is false, so x=-2 is not our solution
(B) x=-1, plug in -1 for x
\(\frac{2}{3}(-1)+\frac{8}{3} = 2^{-1}\)
\(\frac{-2+8}{3} =\frac{1}{2^1}\)
\(\frac{6}{3} =\frac{1}{2}\)
\(2=\frac{1}{2}\)
It is false, so x=-1 is not our solution
(C) x=1, plug in 1 for x
\(\frac{2}{3}(1)+\frac{8}{3} = 2^1\)
\(\frac{2+8}{3} =2\)
\(\frac{10}{3} =2\)
It is false, so x=1 is not our solution
(D) x=2, plug in 2 for x
\(\frac{2}{3}(2)+\frac{8}{3} = 2^2\)
\(\frac{4+8}{3} =4\)
\(\frac{12}{3} =4\)
4 = 4
It is true, so x=2 is our solution
