Question

How do you solve `6( x + 11) = 14x + 42`?

Answer 1

See a solution process below:

Explanation:

First, expand the terms in parenthesis on the left side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

`color(red)(6)(x + 11) = 14x + 42`

`(color(red)(6) xx x) + (color(red)(6) xx 11) = 14x + 42`

`6x + 66 = 14x + 42`

Next, subtract `color(red)(6x)` and `color(blue)(42)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`-color(red)(6x) + 6x + 66 - color(blue)(42) = -color(red)(6x) + 14x + 42 - color(blue)(42)`

`0 + 24 = (-color(red)(6) + 14)x + 0`

`24 = 8x`

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

`24/color(red)(8) = (8x)/color(red)(8)`

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

`3 = x`

`x = 3`