First, multiply each side of the equation by color(red)(60) to eliminate the fraction and keep the equation balanced. Eliminating the fraction will make solving the problem easier to do. color(red)(6) is the lowest common denominator of the two fractions.
color(red)(60)(k - 5/12) = color(red)(60) xx -3/10
(color(red)(60) xx k) - (color(red)(60) xx 5/12) = cancel(color(red)(60))6 xx -3/color(red)(cancel(color(black)(10)))
60k - (cancel(color(red)(60))5 xx 5/color(red)(cancel(color(black)(12)))) = -18
60k - 25 = -18
Next, add color(red)(25) to each side of the equation to isolate the k term while keeping the equation balanced:
60k - 25 + color(red)(25) = -18 + color(red)(25)
60k - 0 = 7
60k = 7
Now, divide each side of the equation by color(red)(60) to solve for k while keeping the equation balanced:
(60k)/color(red)(60) = 7/color(red)(60)
(color(red)(cancel(color(black)(60)))k)/cancel(color(red)(60)) = 7/60
k = 7/60
