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

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

Answer 2

2/3x + 8/3 = 2x

.66x + 2.66 = 2x

-.66x            -.66

2.66 = 1.34x

/1.34    /1.34

x = 0.503
 
I hope that helped!