Question

How do you solve `4+ 6( x + 2) = 2- ( x - 3)`?

Answer 1

See a solution process below:

Explanation:

First, remove the terms in parenthesis on the right side of the equation being careful to manage the signs of the individual terms correctly:

`4 + 6(x + 2) = 2 - x + 3`

`4 + 6(x + 2) = 2 + 3 - x`

`4 + 6(x + 2) = 5 - x`

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

`4 + color(red)(6)(x + 2) = 5 - x`

`4 + (color(red)(6) xx x) + (color(red)(6) xx 2) = 5 - x`

`4 + 6x + 12 = 5 - x`

`4 + 12 + 6x = 5 - x`

`16 + 6x = 5 - x`

Then, subtract `color(red)(16)` and add `color(blue)(x)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`-color(red)(16) + 16 + 6x + color(blue)(x) = -color(red)(16) + 5 - x + color(blue)(x)`

`0 + 6x + color(blue)(1x) = -11 - 0`

`(6 + color(blue)(1))x = -11`

`7x = -11`

Now, divide each side of the equation by `color(red)(7)` to solve for `x` while keeping the equation balanced:

`(7x)/color(red)(7) = -11/color(red)(7)`

`(color(red)(cancel(color(black)(7)))x)/cancel(color(red)(7)) = -11/7`

`x = -11/7`