Answer: [tex]i=5[/tex]
Step-by-step explanation:
[tex]\frac{9}{8}(4i+64)=\frac{5}{8} i+\frac{731}{8}[/tex]
Let's begin by distributing the [tex]\frac{9}{8}[/tex] .
[tex](\frac{9}{8} )(4i)+(\frac{9}{8} )(64)=\frac{5}{8} i+\frac{731}{8}[/tex]
We can simplify 4 and 8.
4/4=1
8/4=2
[tex](\frac{9}{2})(i)[/tex]
We can also simplify 64 and 8.
64/8=8
8/8=1
[tex](9)(8)[/tex]
So our equation would be;
[tex](\frac{9}{2}) (i)+(9)(8)=\frac{5}{8}i+\frac{731}{8}[/tex]
Solve the parentheses.
[tex]\frac{9}{2}i+72=\frac{5}{8} i+\frac{731}{8}[/tex]
Substract [tex]\frac{5}{8}i[/tex] 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.
[tex](-\frac{5}{8}i-72)+\frac{9}{2}i+72=\frac{5}{8} i+\frac{731}{8}+(-\frac{5}{8}i-72)[/tex]
Solve;
[tex]\frac{9}{2}i-\frac{5}{8}i=\frac{731}{8}-72[/tex]
Solve the substraction on both sides.
[tex]\frac{(9)(8)-(2)(5)}{(2)(8)} i=\frac{731-(8)(72)}{8}[/tex]
[tex]\frac{72-10}{16}i=\frac{731-576}{8}[/tex]
[tex]\frac{62}{16}i=\frac{155}{8}[/tex]
Simplify 62 and 16.
62/2=31
16/2=8
[tex]\frac{31}{8}i=\frac{155}{8}[/tex]
Multiply on both sides by the reciprocal of [tex]\frac{31}{8}[/tex] to isolate i.
The reciprocal is the inverse fraction. [tex]\frac{8}{31}[/tex]
[tex](\frac{8}{31} )(\frac{31}{8}i)=(\frac{155}{8}) (\frac{8}{31} )[/tex]
In the right side, you can simplify 8 and 8 leaving;
[tex]i=\frac{155}{31}[/tex]
[tex]i=5[/tex] This is your result.
