Question

How do you solve `2( b - 4) = 8b - 11`?

Answer 1

See the entire solution process below:

Explanation:

First, expand the terms in parenthesis on the left side of the equation by multiplying each term in the parenthesis by `2`:

`2b - 8 = 8b - 11`

Next, subtract `color(red)(2b)` and add `color(blue)(11)` to each side of the equation to isolate the `b` term while keeping the equation balanced:

`2b - 8 - color(red)(2b) + color(blue)(11) = 8b - 11 - color(red)(2b) + color(blue)(11)`

`2b - color(red)(2b) - 8 + color(blue)(11) = 8b - color(red)(2b) - 11 + color(blue)(11)`

`0 + 3 = (8 - 2)b - 0`

`3 = 6b`

Now, divide each side of the equation by `color(red)(6)` to solve for `b` while keeping the equation balanced:

`3/color(red)(6) = (6b)/color(red)(6)`

`1/2 = (color(red)(cancel(color(black)(6)))b)/cancel(color(red)(6))`

`1/2 = b`

`b = 1/2`