How do you solve #v/(v-9)=10/6#?

1 Answer

Answer:

#v = 22.5#
Get rid of the denominators by multiplying both sides by #color(red)(6 (v -9))# Then solve for #v#

Explanation:

By multiplying both sides by the LCD of both denominators, the denominators are eliminated and the problem is simplified.

#color(red)(6( v-9))xx v/(v-9) = color(red)(6( v-9)) xx 10 / 6#

Because # ((v-9))/(( v-9)) = 1 and 6/6 = 1# this allows us to cancel.

#color(red)(6cancel(( v-9)))xx v/cancel(v-9) = color(red)(cancel6( v-9)) xx 10/cancel6#

This leaves the equation as

# 6 ( v )# = # (v-9) xx 10#

Multiplying across the parenthesis gives

#6v = 10 v - 90#

Subtract #10v# from both sides. (Remember when you're trying to solve or find something always work backwards. PE SAD M -4

Do Parathesis and exponent first then do subtraction and addition from left to right, before doing division and multiplication from left to right.

#6v - 10v = 10v - 10v - 90#

this leaves

#-4v = - 90#

Now divide both sides by #-4 # to solve for #v#

# (-4 v)/-4 = (-90)/(-4)#

this gives

#v = + 22.5#