Question

How do you solve `\frac { 16} { x } = \frac { 5} { 2}`?

Answer 1

See a solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(2)color(blue)(x)` to eliminate the fractions while keeping the equation balanced:

`color(red)(2)color(blue)(x) xx 16/x = color(red)(2)color(blue)(x) xx 5/2`

`color(red)(2)cancel(color(blue)(x)) xx 16/color(blue)(cancel(color(black)(x))) = cancel(color(red)(2))color(blue)(x) xx 5/color(red)(cancel(color(black)(2)))`

`32 = 5x`

Now, divide each side of the equation by `color(red)(5)` to solve for `x` while keeping the equation balanced:

`32/color(red)(5) = (5x)/color(red)(5)`

`32/5 = (color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5))`

`32/5 = x`

`x = 32/5`

Or

`x = 6.4`

Answer 2

`x=32/5`

Explanation:

`"given a fraction equal to a fraction, we can solve using"`
`color(blue)"cross-multiplication"`

`color(blue)(16)/color(red)(x)X^=color(red)(5)/color(blue)(2)`

`"multiply terms in blue and terms in red together and equate"`

`color(red)(5x)=color(blue)(16xx2)`

`rArr5x=32`

`"divide both sides by 5"`

`(cancel(5) x)/cancel(5)=32/5`

`rArrx=32/5`

`color(blue)"As a check"`

Substitute this value into the left side and if equal to the right side then it is the solution.

`16/(32/5)=cancel(16)^1/1xx5/cancel(32)^2=5/2=" right side"`

`rArrx=32/5" is the solution"`