Question

How do you solve `9(4b - 1) = 2(9b + 3)`?

Answer 1

9(4b - 1) = 2(9b + 3)

Expanding the brackets we have:

36b - 9 = 18b + 6

Subtracting 18b we have:

18b - 9 = 6

Adding 9 we have:

18b = 15

Dividing by 18 we have:

`b = 15/18`

or, `b = 5/6`

:)>

Answer 2

See the solution process below: `b = 5/6`

Explanation:

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

`color(red)(9)(4b - 1) = color(blue)(2)(9b + 3)`

`(color(red)(9) * 4b) - (color(red)(9) * 1) = (color(blue)(2) * 9b) + (color(blue)(2) * 3)`

`36b - 9 = 18b + 6`

Next, add `color(red)(9)` and subtract `color(blue)(18b)` from each side of the equation to isolate the `b` term while keeping the equation balanced:

`36b - 9 + color(red)(9) - color(blue)(18b) = 18b + 6 + color(red)(9) - color(blue)(18b)`

`36b - color(blue)(18b) - 9 + color(red)(9) = 18b - color(blue)(18b) + 6 + color(red)(9)`

`(36 - color(blue)(18))b - 0 = 0 + 15`

`18b = 15`

Now, divide each side of the equation by `color(red)(18)` to solve for `b` while keeping the equation balanced:

`(18b)/color(red)(18) = 15/color(red)(18)`

`(color(red)(cancel(color(black)(18)))b)/cancel(color(red)(18)) = (3 xx 5)/color(red)(3 xx 6)`

`b = (color(red)(cancel(color(black)(3))) xx 5)/color(red)(color(black)(cancel(color(red)(3))) xx 6)`

`b = 5/6`