Question

solve for t.
\\(\frac{5}{4}t = \frac{1}{2}t - 3 + \frac{2}{3}t\\)
\\(t = \\)
submit

Explanation:

Step1: Combine like terms on the right

First, we need to combine the \( t \)-terms on the right side of the equation. The terms with \( t \) are \( \frac{1}{2}t \) and \( \frac{2}{3}t \). To add these, we find a common denominator, which is 6. So, \( \frac{1}{2}t=\frac{3}{6}t \) and \( \frac{2}{3}t = \frac{4}{6}t \). Adding them together: \( \frac{3}{6}t+\frac{4}{6}t=\frac{7}{6}t \). Now the equation becomes:
\[
\frac{5}{4}t=\frac{7}{6}t - 3
\]

Step2: Subtract \( \frac{7}{6}t \) from both sides

To get all the \( t \)-terms on one side, we subtract \( \frac{7}{6}t \) from both sides. First, find a common denominator for \( \frac{5}{4}t \) and \( \frac{7}{6}t \), which is 12. So, \( \frac{5}{4}t=\frac{15}{12}t \) and \( \frac{7}{6}t=\frac{14}{12}t \). Subtracting:
\[
\frac{15}{12}t-\frac{14}{12}t=\frac{1}{12}t
\]
And the right side becomes \( - 3 \). So now the equation is:
\[
\frac{1}{12}t=-3
\]

Step3: Solve for \( t \)

To solve for \( t \), we multiply both sides of the equation by 12 (the reciprocal of \( \frac{1}{12} \)):
\[
t=-3\times12
\]
\[
t = - 36
\]

Answer:

\( -36 \)