Question #248ba

1 Answer
Mar 17, 2017

Answer:

#x=-1/5#

Explanation:

#color(blue)("Reduce the fractions")#

#(cancel9^color(red)(1)(1-2x))/(cancel9^color(red)1(1+2x))-(cancel7^color(red)(1)(2x))/(cancel7^color(red)1(1+2x))=3#

#(1-2x)/(1+2x)-(2x)/(1+2x)=3#

#color(blue)("Carry out the subtraction of the fractions")#

Because the denominator (the bottom number) is the same for each fraction, you simply subtract the second numerator (top number of the fraction) from the first:

#((1-2x)-(2x))/(1+2x)=3#

#(1-4x)/(1+2x)=3#

#color(blue)("Remove the denominator")#

By multiplying both sides of the equals sign by #1+2x#, we can remove the denominator:

#(1-4x)/cancel(1+2x)^color(red)(1)xx(cancel(1+2x)^color(red)1)=3(1+2x)#

#1-4x=3+6x#

#color(blue)("Rearrange")#

Add #4x# to both sides and subtract #3# from both sides gives:

#1-4x+4x-3=3+6x+4x-3#

#color(blue)("Collect like terms")#

#1-3=6x+4x#

#-2=10x#

#color(blue)("Find the answer")#

Divide both sides through by 10, to give:

#-2/(10)=x#

#x=-1/5#