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](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%20x%2B%5Cfrac%7B8%7D%7B3%7D%20%3D2%5Ex)
Let plug in each option and check
(A) x=-2, plug in -2 for x
![\frac{2}{3}(-2)+\frac{8}{3} = 2^{-2}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%28-2%29%2B%5Cfrac%7B8%7D%7B3%7D%20%3D%202%5E%7B-2%7D)
![\frac{-4+8}{3} =\frac{1}{2^2}](https://tex.z-dn.net/?f=%5Cfrac%7B-4%2B8%7D%7B3%7D%20%3D%5Cfrac%7B1%7D%7B2%5E2%7D)
![\frac{4}{3} =\frac{1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%20%3D%5Cfrac%7B1%7D%7B4%7D)
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}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%28-1%29%2B%5Cfrac%7B8%7D%7B3%7D%20%3D%202%5E%7B-1%7D)
![\frac{-2+8}{3} =\frac{1}{2^1}](https://tex.z-dn.net/?f=%5Cfrac%7B-2%2B8%7D%7B3%7D%20%3D%5Cfrac%7B1%7D%7B2%5E1%7D)
![\frac{6}{3} =\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B3%7D%20%3D%5Cfrac%7B1%7D%7B2%7D)
![2=\frac{1}{2}](https://tex.z-dn.net/?f=2%3D%5Cfrac%7B1%7D%7B2%7D)
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](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%281%29%2B%5Cfrac%7B8%7D%7B3%7D%20%3D%202%5E1)
![\frac{2+8}{3} =2](https://tex.z-dn.net/?f=%5Cfrac%7B2%2B8%7D%7B3%7D%20%3D2)
![\frac{10}{3} =2](https://tex.z-dn.net/?f=%5Cfrac%7B10%7D%7B3%7D%20%3D2)
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](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%282%29%2B%5Cfrac%7B8%7D%7B3%7D%20%3D%202%5E2)
![\frac{4+8}{3} =4](https://tex.z-dn.net/?f=%5Cfrac%7B4%2B8%7D%7B3%7D%20%3D4)
![\frac{12}{3} =4](https://tex.z-dn.net/?f=%5Cfrac%7B12%7D%7B3%7D%20%3D4)
4 = 4
It is true, so x=2 is our solution