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
[tex]\frac{2}{3} x+\frac{8}{3} =2^x[/tex]
Let plug in each option and check
(A) x=-2, plug in -2 for x
[tex]\frac{2}{3}(-2)+\frac{8}{3} = 2^{-2}[/tex]
[tex]\frac{-4+8}{3} =\frac{1}{2^2}[/tex]
[tex]\frac{4}{3} =\frac{1}{4}[/tex]
It is false, so x=-2 is not our solution
(B) x=-1, plug in -1 for x
[tex]\frac{2}{3}(-1)+\frac{8}{3} = 2^{-1}[/tex]
[tex]\frac{-2+8}{3} =\frac{1}{2^1}[/tex]
[tex]\frac{6}{3} =\frac{1}{2}[/tex]
[tex]2=\frac{1}{2}[/tex]
It is false, so x=-1 is not our solution
(C) x=1, plug in 1 for x
[tex]\frac{2}{3}(1)+\frac{8}{3} = 2^1[/tex]
[tex]\frac{2+8}{3} =2[/tex]
[tex]\frac{10}{3} =2[/tex]
It is false, so x=1 is not our solution
(D) x=2, plug in 2 for x
[tex]\frac{2}{3}(2)+\frac{8}{3} = 2^2[/tex]
[tex]\frac{4+8}{3} =4[/tex]
[tex]\frac{12}{3} =4[/tex]
4 = 4
It is true, so x=2 is our solution
