How do you solve $\frac{x + 1}{4} = 2 - (\frac{x + 2}{5})$ $(x + 1) / 4 = 2 - ( (x + 2) / 5)$ ?

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Answer 1 · 2017-08-29T16:28:18

See a solution process below:

First, multiply each side of the equation by $20$ $color(red)(20)$ to eliminate the fractions while keeping the equation balanced:

$20 (\frac{x + 1}{4}) = 20 (2 - (\frac{x + 2}{5}))$ $color(red)(20)((x + 1)/4) = color(red)(20)(2 - ((x + 2)/5))$

$cancel(color(red)(20))5((x + 1)/color(red)(cancel(color(black)(4)))) = (color(red)(20) xx 2) - (color(red)(20) xx ((x + 2)/5))$

$5(x + 1) = 40 - (cancel(color(red)(20))4 xx ((x + 2)/color(red)(cancel(color(black)(5)))))$

$(5 xx x) + (5 xx 1) = 40 - 4(x + 2)$

$5x + 5 = 40 - (4 xx x) - (4 xx 2)$

$5x + 5 = 40 - 4x - 8$

$5x + 5 = -4x - 8 + 40$

$5x + 5 = -4x + 32$

Next, subtract $color(red)(5)$ and add $color(blue)(4x)$ to each side of the equation to isolate the $x$ term while keeping the equation balanced:

$color(blue)(4x) + 5x + 5 - color(red)(5) = color(blue)(4x) - 4x + 32 - color(red)(5)$

$(color(blue)(4) + 5)x + 0 = 0 + 27$

$9x = 27$

Now, divide each side of the equation by $color(red)(9)$ to solve for $x$ while keeping the equation balanced:

$(9x)/color(red)(9) = 27/color(red)(9)$

$(color(red)(cancel(color(black)(9)))x)/cancel(color(red)(9)) = 3$

$x = 3$

How do you solve (x + 1) / 4 = 2 - ( (x + 2) / 5) x+14=2−(x+25)(x + 1) / 4 = 2 - ( (x + 2) / 5) ?