2. 5t – 3 = 3t – 5

Given 5t – 3 = 3t – 5
\(\Rightarrow\) 5t – 3t – 3 = -5 (Transposing 3t to LHS)

\(\Rightarrow\)2t = -5 + 3 (Transposing -3 to RHS)

\(\Rightarrow\)2t = -2

\(\Rightarrow\) t = -2 ÷ 2

\(\Rightarrow\) t = -1

Hence, t = -1 is the required solution.

Checking:

5t – 3 = 3t – 5

Substitute t = -1 in the given equation, we have

LHS = 5t – 3 = 5 × (-1)-3 = -5 – 3 = -8

RHS = 3t – 5 = 3 × (-1) – 5 = -3 – 5 = -8

LHS = RHS

Hence, t = -1 is the required solution.