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

2 Answers
Apr 30, 2017

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

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Apr 30, 2017

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