Question

9/8(4i + 64) = 5/8i + 731/8
What does i equal?

Answer 1

Answer:
`i=5`

Explanation:

`(9)/(8)(4i+64)=(5)/(8) i+(731)/(8)`

Let's begin by distributing the
`(9)/(8)` .

`((9)/(8) )(4i)+((9)/(8) )(64)=(5)/(8) i+(731)/(8)`

We can simplify 4 and 8.

4/4=1

8/4=2

`((9)/(2))(i)`

We can also simplify 64 and 8.

64/8=8

8/8=1

`(9)(8)`

So our equation would be;

`((9)/(2)) (i)+(9)(8)=(5)/(8)i+(731)/(8)`

Solve the parentheses.

`(9)/(2)i+72=(5)/(8) i+(731)/(8)`

Substract
`(5)/(8)i` on both sides to isolate the terms with ''i'' in the left side. And also substract 72 on both sides to move the independent terms to the right side.

`(-(5)/(8)i-72)+(9)/(2)i+72=(5)/(8) i+(731)/(8)+(-(5)/(8)i-72)`

Solve;

`(9)/(2)i-(5)/(8)i=(731)/(8)-72`

Solve the substraction on both sides.

`((9)(8)-(2)(5))/((2)(8)) i=(731-(8)(72))/(8)`

`(72-10)/(16)i=(731-576)/(8)`

`(62)/(16)i=(155)/(8)`

Simplify 62 and 16.

62/2=31

16/2=8

`(31)/(8)i=(155)/(8)`

Multiply on both sides by the reciprocal of
`(31)/(8)` to isolate i.

The reciprocal is the inverse fraction.
`(8)/(31)`

`((8)/(31) )((31)/(8)i)=((155)/(8)) ((8)/(31) )`

In the right side, you can simplify 8 and 8 leaving;

`i=(155)/(31)`

`i=5` This is your result.