Question

How do you solve `\frac { 6x - 7} { 4} + \frac { 3x - 5} { 7} = \frac { 5x + 7} { 28}`?

Answer 1

See the entire solution process below:`x = 76/49`

Explanation:

First, multiply both sides for the equation by `color(red)(28)` to eliminate the fractions while keeping the equation balanced:

`color(red)(28)((6x - 7)/4 + (3x - 5)/7) = color(red)(28) xx (5x + 7)/28`

`(color(red)(28) xx (6x - 7)/4) + (color(red)(28) xx (3x - 5)/7) = cancel(color(red)(28)) xx (5x + 7)/color(red)(cancel(color(black)(28)))`

`(cancel(color(red)(28))7 xx (6x - 7)/color(red)(cancel(color(black)(4)))) + (cancel(color(red)(28))4 xx (3x - 5)/color(red)(cancel(color(black)(7)))) = 5x + 7`

`7(6x - 7) + 4(3x - 5) = 5x + 7`

`42x - 49 + 12x - 20 = 5x + 7`

`42x + 12x - 49 - 20 = 5x + 7`

`54x - 69 = 5x + 7`

Next, subtract `color(red)(5x)` and add `color(blue)(69)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`54x - 69 + color(blue)(69) - color(red)(5x) = 5x + 7 + color(blue)(69) - color(red)(5x)`

`54x - color(red)(5x) - 69 + color(blue)(69) = 5x - color(red)(5x) + 7 + color(blue)(69)`

`54x - 5x - 0 = 0 + 7 + 69`

`49x = 76`

Now, divide each side of the equation by `color(red)(49)` to solve for `x` while keeping the equation balanced:

`(49x)/color(red)(49) = 76/color(red)(49)`

`(color(red)(cancel(color(black)(49)))x)/cancel(color(red)(49)) = 76/49`

`x = 76/49`