How do you solve $\frac { w - 1} { 5} = \frac { w + 2} { 2}$ ?

Question

1382 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-23T22:52:54

See the entire solution process below:

First, multiply each side of the equation by $color(red)(10)$ to eliminate the fractions while keeping the equation balanced:

$color(red)(10) xx (w - 1)/5 = color(red)(10) xx (w + 2)/2$

$cancel(color(red)(10))2 xx (w - 1)/color(red)(cancel(color(black)(5))) = cancel(color(red)(10))5 xx (w + 2)/color(red)(cancel(color(black)(2)))$

$2(w - 1) = 5(w + 2)$

Next, eliminate the parenthesis on each side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

$(2 xx w) - (2 xx 1) = (5 xx w) + (5 xx 2)$

$2w - 2 = 5w + 10$

Then, subtract $color(red)(2w)$ and $color(blue)(10)$ from each side of the equation to isolate the $w$ term while keeping the equation balanced:

$2w - 2 - color(red)(2w) - color(blue)(10) = 5w + 10 - color(red)(2w) - color(blue)(10)$

$2w - color(red)(2w) - 2 - color(blue)(10) = 5w - color(red)(2w) + 10 - color(blue)(10)$

$0 - 12 = 3w + 0$

$-12 = 3w$

Now, divide each side of the equation by $color(red)(3)$ to solve for $w$ while keeping the equation balanced:

$(-12)/color(red)(3) = (3w)/color(red)(3)$

$-4 = (color(red)(cancel(color(black)(3)))w)/cancel(color(red)(3))$

$-4 = w$

$w = -4$

How do you solve \frac { w - 1} { 5} = \frac { w + 2} { 2}\frac { w - 1} { 5} = \frac { w + 2} { 2}?