How do you solve #1+ \frac { 1} { x - 7} = \frac { 4x } { x - 7}#?

1 Answer
Nov 28, 2016

#x = -2#

Explanation:

#1 + 1/(x-7) = (4x)/(x-7)#

Subtract #1/(x-7)# from both sides of the #=# sign.

#1 = (4x)/(x-7) - 1/(x-7)#

Since both of the right side fractions have the same denominator #(x-7)#, the subtraction of the second from the first can be written as:

#1 = (4x-1)/(x-7)#

Now you can multiply both sides by #x-7#.

#1(x-7) = 4x-1#

Multiply out the bracket.

#x-7 =4x-1#

Subtract #x# from both sides:

#-7 = 3x - 1#

Add #1# to both sides.

#-6 = 3x#

Divide both sides by #3#.

#-2 = x#