Question

An equation is shown below:

3/2x + 7/2 = 2^x

X = 1

X = 3

X = 5

X = 8

Answer 1

x=3 because

`(3)/(2) * 3 = (9)/(2)`

`(9)/(2) + (7)/(2) = 8`
And

`{2}^(3) = 8`
So the equation is balanced

Answer 2

Option - 2, The solution of the equation is at x=3.

Explanation:

Given : Equation
`(3)/(2)x+(7)/(2)=2^x`

To find : The point which satisfy the equation?

Solution :

To find the point we put all the given points one by one which satisfy the equation is the required point.

`(3)/(2)x+(7)/(2)=2^x`

1) Put x=1,

`(3)/(2)(1)+(7)/(2)=2^1`

`(3+7)/(2)=2`

`(10)/(2)=2`

`5\\eq2`

x=1 is not a point.

2) Put x=3,

`(3)/(2)(3)+(7)/(2)=2^3`

`(9+7)/(2)=8`

`(16)/(2)=8`

`8=8`

x=3 is a point satisfying equation.

3) Put x=5,

`(3)/(2)(5)+(7)/(2)=2^5`

`(15+7)/(2)=32`

`(22)/(2)=32`

`11\\eq32`

x=5 is not a point.

4) Put x=8,

`(3)/(2)(8)+(7)/(2)=2^8`

`(24+7)/(2)=256`

`(31)/(2)=256`

`15.5\\eq256`

x=8 is not a point.

Therefore, The solution of the equation is at x=3.