Question

How do you solve `\frac { 3x + 16} { 5} + \frac { x + 20} { 7} = 12`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(35)` to eliminate the fractions while keeping the equation balanced:

`color(red)(35)((3x + 16)/5 + (x + 20)/7) = color(red)(35) xx 12`

`(color(red)(35) xx (3x + 16)/5) + (color(red)(35) xx (x + 20)/7) = 420`

`(cancel(color(red)(35))7 xx (3x + 16)/color(red)(cancel(color(black)(5)))) + (cancel(color(red)(35))5 xx (x + 20)/color(red)(cancel(color(black)(7)))) = 420`

`7(3x + 16) + 5(x + 20) = 420`

Next, expand the terms in parenthesis, group and combine like terms on the left side of the equation:

`(7 xx 3x) + (7 xx 16) + (5 xx x) + 5 xx 20) = 420`

`21x + 112 + 5x + 100 = 420`

`21x + 5x + 112 + 100 = 420`

`26x + 212 = 420`

Then, subtract `color(red)(212)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`26x + 212 - color(red)(212) = 420 - color(red)(212)`

`26x + 0 = 208`

`26x = 208`

Now, divide each side of the equation by `color(red)(26)` to solve for `x` while keeping the equation balanced:

`(26x)/color(red)(26) = 208/color(red)(26)`

`(color(red)(cancel(color(black)(26)))x)/cancel(color(red)(26)) = 8`

`x = 8`