Firstly, foil -(k + 1/4) (think of the minus sign as -1):
[tex] \frac{2}{3}k-k-\frac{1}{4}=\frac{1}{12}k+\frac{4}{12} [/tex]
Next, combine like terms:
[tex] -\frac{1}{3}k-\frac{1}{4}=\frac{1}{12}k+\frac{4}{12} [/tex]
Next, we have to add 1/3k on both sides, but first we have to find the LCD, or lowest common denominator, of 3 and 12. To do this, list the multiples of both and the lowest one they share is their LCD. In this case, the LCD is 12. Multiply both sides of -1/3 by 4/4 and 1/12 by 1/1:
[tex] -\frac{1}{3}\times \frac{4}{4}=-\frac{4}{12}\\\\\frac{1}{12}\times \frac{1}{1}=\frac{1}{12}\\\\-\frac{4}{12}k-\frac{1}{4}=\frac{1}{12}k+\frac{4}{12} [/tex]
Now add 4/12k on both sides of the equation:
[tex] -\frac{1}{4}=\frac{5}{12}k+\frac{4}{12} [/tex]
Next, to subtract 4/12 on both sides we need to find the LCD of 4 and 12. It's the similar process as we did with 12 and 3. This time the LCD is also 12. Multiply both sides of -1/4 by 3/3 and 4/12 by 1/1:
[tex] -\frac{1}{4}\times \frac{3}{3}=-\frac{3}{12}\\\\\frac{4}{12}\times \frac{1}{1}=\frac{4}{12}\\\\-\frac{3}{12}=\frac{5}{12}k+\frac{4}{12} [/tex]
Now subtract 4/12 on both sides:
[tex] -\frac{7}{12}=\frac{5}{12}k [/tex]
Lastly, multiply both sides by 12/5, and your answer will be:
[tex] -\frac{84}{60}=-\frac{7}{5}=k [/tex]
