Question

How do you evaluate `3g + 4( - 6+ 2g ) = 1- g`?

Answer 1

See a solution process below:

Explanation:

First, expand the terms in parenthesis by multiplying each of the terms within the parenthesis by the term outside the parenthesis:

`3g + color(red)(4)(color(blue)(-6) + color(blue)(2g)) = 1 - g`

`3g + (color(red)(4) xx color(blue)(-6)) + (color(red)(4) xx color(blue)(2g)) = 1 - g`

`3g + (-24) + 8g = 1 - g`

`3g - 24 + 8g = 1 - g`

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

`3g + 8g - 24 = 1 - g`

`(3 + 8)g - 24 = 1 - g`

`11g - 24 = 1 - g`

Then, add `color(red)(24)` and `color(blue)(g)` to each side of the equation to isolate the `g` term while keeping the equation balanced:

`11g - 24 + color(red)(24) + color(blue)(g) = 1 - g + color(red)(24) + color(blue)(g)`

`11g + color(blue)(g) - 24 + color(red)(24) = 1 + color(red)(24) - g + color(blue)(g)`

`11g + 1color(blue)(g) - 0 = 25 - 0`

`(11 + 1)color(blue)(g) = 25`

`12g = 25`

Now, divide each side of the equation by `color(red)(12)` to solve for `g` while keeping the equation balanced:

`(12g)/color(red)(12) = 25/color(red)(12)`

`(color(red)(cancel(color(black)(12)))g)/cancel(color(red)(12)) = 25/12`

`g = 25/12`