Question

How do you solve `\frac { 1+ 3x } { 7} + \frac { 2- x } { 5} = \frac { 3} { 35}`?

Answer 1

x = -2

Explanation:

First, you want to multiply both sides by 35. This eliminates the need for a denominator.

`(1+3x)/7 + (2-x)/5 = 3/35 ->`

`35*((1+3x)/7 + (2-x)/5) =35*(3/35) ->`

`5*(1+3x) + 7*(2-x) = 3`

Next, factor out your terms and simplify on the left side.

`5*(1+3x) + 7*(2-x) = 3 ->`

`5 + 15x + 14 - 7x = 3 ->`

`8x + 19 = 3`

Next, subtract 19 from each side.

`8x + 19 = 3 ->`

`8x + 19 - 19= 3 - 19 ->`

`8x = -16`

Finally, divide by 8 to get your answer.

`8x = -16 ->`

`(8x)/8 = (-16)/8 ->`

`x = -2`

There is an optional step. If you want to, plug -2 into the equation to check your answer.

`(1+3(-2))/7 + (2-(-2))/5 = 3/35 ->`

`(1-6)/7 + 4/5 = 3/35 ->`

`-5/7 + 4/5 = 3/35 ->`

`(5*-5)/(5*7) + (7*4)/(7*5) = 3/35 ->`

`-25/35 + 28/35 = 3/35 ->`

`3/35 = 3/35`