Question

How do you solve `\frac { ( 8- n ) } { 7} = \frac { 4} { 3}`?

Answer 1

`n = -4/3`

Explanation:

Step 1) Multiple each side of the equation by 21 (common denominator of each fraction) to eliminate the fraction and make the equation easier to work with.
Step 2) Expand the terms in the parenthesis
Step 3) Solve for `n` while keeping the equation balanced

`21(8 - n)/7 = 21(4/3)`

`3(8 - n) = 7 * 4`

`24 - 3n = 28`

`24 - 3n - 24 = 28 - 24`

`-3n = 4`

`-3n/-3 = 4/-3`

`n = -4/3`

Answer 2

`n=-4/3`

Explanation:

When we have a fraction equal to another fraction we can solve using the method of `color(blue)"cross-multiplication."` That is.

`((color(red)(8-n)))/color(blue)(7)=color(blue)(4)/color(red)(3)`

Now, multiply the values at either end of an imaginary cross (X) placed over the = sign and equate them.
That is multiply the values in `color(red)"red"` together, the values in `color(blue)"blue"` together and equate them.

`(color(red)(8-n))xxcolor(red)(3)=color(blue)(4)xxcolor(blue)(7)`

`rArr3(8-n)=28`

distribute the bracket.

`24-3n=28`

subtract 24 from both sides.

`cancel(24)cancel(-24)-3n=28-24`

`rArr-3n=4`

To solve for n, divide both sides by - 3.

`(cancel(-3) n)/cancel(-3)=4/(-3)`

`rArrn=-4/3" is the solution"`