Question

How do you solve `\frac { x + 5} { 2} = \frac { 38} { 16}`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(16)` (this is the LCD of the two fractions) to eliminate the fractions while keeping the equation balanced:

`cancel(color(red)(16))8 xx (x + 5)/color(red)(cancel(color(black)(2))) = cancel(color(red)(16)) xx 38/color(red)(cancel(color(black)(16)))`

`8(x + 5) = 38`

`(8 xx x) + (8 xx 5) = 38`

`8x + 40 = 38`

Next, subtract `color(red)(40)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`8x + 40 - color(red)(40) = 38 - color(red)(40)`

`8x + 0 = -2`

`8x = -2`

Now, divide each side of the equation by `color(red)(8)` to solve for `x` while keeping the equation balanced:

`(8x)/color(red)(8) = -2/color(red)(8)`

`(color(red)(cancel(color(black)(8)))x)/cancel(color(red)(8)) = -2/color(red)(8)`

`x = -1/4`