Question

How do you solve `\frac { 3x + 15+ ( 11x - 5) } { 2} = 47`?

Answer 1

See the entire solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(2)` to eliminate the fraction and keep the equation balanced:

`color(red)(2) xx (3x + 15 + (11x - 5))/2 = color(red)(2) xx 47`

`cancel(color(red)(2)) xx (3x + 15 + (11x - 5))/color(red)(cancel(color(black)(2))) = 94`

`3x + 15 + (11x - 5) = 94`

Next, remove the terms on the left hand side of the equation from parenthesis, group and combine like terms:

`3x + 15 + 11x - 5 = 94`

`3x + 11x + 15 - 5 = 94`

`(3 + 11)x + (15 - 5) = 94`

`14x + 10 = 94`

Then, subtract `color(red)(10)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`14x + 10 - color(red)(10) = 94 - color(red)(10)`

`14x + 0 = 84`

`14x = 84`

Now, divide each side of the equation by `color(red)(14)` to solve for `x` while keeping the equation balanced:

`(14x)/color(red)(14) = 84/color(red)(14)`

`(color(red)(cancel(color(black)(14)))x)/cancel(color(red)(14)) = 6`

`x = 6`