Question

Solve the linear equation: \(\frac{3t-2}{4}-\frac{2t+3}{3}=\frac{2}{3}-t\)

Answer 1

\(\frac{3t-2}{4}-\frac{2t+3}{3}=\frac{2}{3}-t\)
L.C.M. of the denominators, \(3\) and \(4\), is \(12\).
Multiplying both sides by \(12\), we obtain
\(3(3t - 2) - 4(2t + 3) = 8 - 12t\)
\(\Rightarrow\) \(9t - 6 - 8t - 12 = 8 - 12t\) (Opening the brackets)
\(\Rightarrow\) \(9t - 8t + 12t = 8 + 6 + 12\)
\(\Rightarrow\) \(13t = 26\)
\(\Rightarrow\) \(t\) = \(\frac{26}{13}\)
\(\Rightarrow\) \(t = 2\)