Question

How do you solve `\frac{x + 7}{x} = \frac{7}{9}`?

Answer 1

`x = -63/2 or -31.5`

Explanation:

`(x+7)/ x = 7/9`

There may be more complex, quicker ways to solve this, but by simply moving around the numbers in order to isolate `x`, we can solve this question.

`(x+7)/x xx 9= 7/color(red)(cancel(color(black)(9))) color(red)(cancel(xx 9))`

`((x+7) xx 9)/ x = 7`

`(9x + 63)/ color(red)(cancel(color(black)(x))) color(red)(cancel(xx x)) = 7 color(red)(xx x)`

`9x + 63 color(red)(-7x)= color(red)(cancel(color(black)(7x) -7x))`

`2x color(red)(cancel(color(black)(+63) -63))= 0 color(red)(-63)`

`(color(red)(cancel(color(black)(2)))x)/color(red)(cancel(2)) = -63/color(red)(2)`

`color(blue)(x = -63/2)`

`color(blue)(x = -31.5)`

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We can check this by substituting the result for the Pronumeral.

`(x+7)/ x = 7/9`

`(-31.5 + 7)/ -31.5 = 7/9`

`(24.5 color(red)(xx 2))/ (31.5 color(red)(xx 2)) = 7/9`

`(49 color(red)(-: 7))/(63 color(red)(-: 7)) = 7/9`

`7/9 = 7/9`

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