Question

%7B1%7D%7B12%7Dk%20%2B%20%20%5Cfrac%7B4%7D%7B12%7D%20%20%20%20%20%5C%5C%20%20%5C%5C%20" id="TexFormula1" title=" \frac{2}{3} k - (k + \frac{1}{4}) = \frac{1}{12}k + \frac{4}{12} \\ \\ " alt=" \frac{2}{3} k - (k + \frac{1}{4}) = \frac{1}{12}k + \frac{4}{12} \\ \\ " align="absmiddle" class="latex-formula">

Answer 1

Firstly, foil -(k + 1/4) (think of the minus sign as -1):

$\frac{2}{3}k-k-\frac{1}{4}=\frac{1}{12}k+\frac{4}{12}$

Next, combine like terms:

$-\frac{1}{3}k-\frac{1}{4}=\frac{1}{12}k+\frac{4}{12}$

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:

$-\frac{1}{3}\times \frac{4}{4}=-\frac{4}{12}\\\\\frac{1}{12}\times \frac{1}{1}=\frac{1}{12}\\\\-\frac{4}{12}k-\frac{1}{4}=\frac{1}{12}k+\frac{4}{12}$

Now add 4/12k on both sides of the equation:

$-\frac{1}{4}=\frac{5}{12}k+\frac{4}{12}$

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:

$-\frac{1}{4}\times \frac{3}{3}=-\frac{3}{12}\\\\\frac{4}{12}\times \frac{1}{1}=\frac{4}{12}\\\\-\frac{3}{12}=\frac{5}{12}k+\frac{4}{12}$

Now subtract 4/12 on both sides:

$-\frac{7}{12}=\frac{5}{12}k$

Lastly, multiply both sides by 12/5, and your answer will be:

$-\frac{84}{60}=-\frac{7}{5}=k$