Question

An equation is shown below: 2 over 3 multiplied by x plus 8 over 3 equals 2 to the power of x What is the solution to the equation?

Answer 1

x=2

Explanation:

I did the test

Answer 2

x=2 is our solution

Explanation:

Given options:

x = −2

x = −1

x = 1

x = 2

Lets plug in each option and check with the given equation

`(2)/(3) x+(8)/(3) =2^x`

Let plug in each option and check

(A) x=-2, plug in -2 for x

`(2)/(3)(-2)+(8)/(3) = 2^(-2)`

`(-4+8)/(3) =(1)/(2^2)`

`(4)/(3) =(1)/(4)`

It is false, so x=-2 is not our solution

(B) x=-1, plug in -1 for x

`(2)/(3)(-1)+(8)/(3) = 2^(-1)`

`(-2+8)/(3) =(1)/(2^1)`

`(6)/(3) =(1)/(2)`

`2=(1)/(2)`

It is false, so x=-1 is not our solution

(C) x=1, plug in 1 for x

`(2)/(3)(1)+(8)/(3) = 2^1`

`(2+8)/(3) =2`

`(10)/(3) =2`

It is false, so x=1 is not our solution

(D) x=2, plug in 2 for x

`(2)/(3)(2)+(8)/(3) = 2^2`

`(4+8)/(3) =4`

`(12)/(3) =4`

4 = 4

It is true, so x=2 is our solution