Question

Question #248ba

Answer 1

`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`