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

1 Answer
Mar 5, 2018

Answer:

#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)#

#ul(color(white)(xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx))#

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#

#ul(color(white)(xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx))#