How do you solve for $r$ in $S=L(1-r)$ ?

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Answer 1 · 2018-03-13T12:54:44

See a solution process below:

First, divide each side of the equation by $color(red)(L)$ to eliminate the need for parenthesis while keeping the equation balanced:

$S/color(red)(L) = (L(1 - r))/color(red)(L)$

$S/L = (color(red)(cancel(color(black)(L)))(1 - r))/cancel(color(red)(L))$

$S/L = 1 - r$

Next subtract $color(red)(S/L)$ and add $color(blue)(r)$ to each side of the equation to solve for $r$ while keeping the equation balanced:

$S/L - color(red)(S/L) + color(blue)(r) = 1 - color(red)(S/L) - r + color(blue)(r)$

$0 + r = 1 - S/L - 0$

$r = 1 - S/L$

Or

$r = L/L - S/L$

$r = (L - S)/L$

How do you solve for rr in S=L(1-r)S=L(1-r)?