How do you solve $1/9 - 2/(3b) = 1/18$ ?

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Answer 1 · 2017-07-18T16:52:28

See a solution process below:

Step 1) Subtract $color(red)(1/9)$ from each side of the equation to isolate the $b$ term while keeping the equation balanced:

$-color(red)(1/9) + 1/9 - 2/(3b) = -color(red)(1/9) + 1/18$

$0 - 2/(3b) = -(2/2 xx color(red)(1/9)) + 1/18$

$-2/(3b) = -2/18 + 1/18$

$-2/(3b) = -1/18$

Step 2) multiply each side of the equation by $color(red)(b)$ to move the $b$ term to the numerator while keeping the equation balanced:

$color(red)(b) xx -2/(3b) = -1/18 xx color(red)(b)$

$cancel(color(red)(b)) xx -2/(3color(red)(cancel(color(black)(b)))) = (-1)/18 xx color(red)(b)$

$(-2)/3 = (-1)/18b$

Step 3) Multiply each side of the equation by $color(red)(-18)$ to solve for $b$ while keeping the equation balanced:

$color(red)(-18) xx (-2)/3 = color(red)(-18) xx (-1)/18b$

$-6cancel(color(red)(-18)) xx (-2)/color(red)(cancel(color(black)(3))) = -1cancel(color(red)(-18)) xx (-1)/color(red)(cancel(color(black)(18)))b$

$12 = b$

$b = 12$

How do you solve 1/9 - 2/(3b) = 1/181/9 - 2/(3b) = 1/18?