How do you solve $\frac{x - 1}{4} - \frac{x}{3} = \frac{1}{12}$ $\frac { x - 1} { 4} - \frac { x } { 3} = \frac { 1} { 12}$ ?

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Answer 1 · 2017-02-19T20:08:55

See the entire solution below: $x = - 4$ $x = -4$

First, multiply each side of the equation by $12$ $color(red)(12)$ to eliminate the fractions while keeping the equation balanced:

$12 (\frac{x - 1}{4} - \frac{x}{3}) = 12 \times \frac{1}{12}$ $color(red)(12)((x - 1)/4 - x/3) = color(red)(12) xx 1/12$

$(color(red)(12) xx (x - 1)/4) - (color(red)(12) xx x/3) = cancel(color(red)(12)) xx 1/color(red)(cancel(color(black)(12)))$

$(cancel(color(red)(12))3 xx (x - 1)/color(red)(cancel(color(black)(4)))) - (cancel(color(red)(12))4 xx x/color(red)(cancel(color(black)(3)))) = 1$

$3(x - 1) - 4x = 1$

Next, expand the terms in parenthesis:

$(3 xx x) - (3 xx 1) - 4x = 1$

$3x - 3 - 4x = 1$

Then, group and combine like terms on the left side of the equation:

$3x - 4x - 3 = 1$

$(3 - 4)x - 3 = 1$

$-1x - 3 = 1$

Next, add $color(red)(3)$ to each side of the equation to isolate the $x$ term while keeping the equation balanced:

$-1x - 3 + color(red)(3) = 1 + color(red)(3)$

$-1x - 0 = 4$

$-1x = 4$

Now, multiply each side of the equation by $color(red)(-1)$ to solve for $x$ while keeping the equation balanced:

$color(red)(-1) xx -1x = color(red)(-1) xx 4$

$1x = -4$

$x = -4$

How do you solve \frac { x - 1} { 4} - \frac { x } { 3} = \frac { 1} { 12}x−14−x3=112\frac { x - 1} { 4} - \frac { x } { 3} = \frac { 1} { 12}?