Answer:
[tex] \rm x = \dfrac{2e - 1}{ {e}^{2} } [/tex]
Step-by-step explanation:
[tex] \rm Solve \: for \: x: \\ \rm \longrightarrow ex + {e}^{ - 1} = 2 \\ \\ \rm \longrightarrow e x + \dfrac{1}{e} = 2 \\ \\ \rm Subtract \: \dfrac{1}{e} \: from \: both \: sides: \\ \rm \longrightarrow e x + \dfrac{1}{e} - \dfrac{1}{e} = 2 - \dfrac{1}{e} \\ \\ \rm \longrightarrow ex = \dfrac{2e}{e} - \dfrac{1}{e} \\ \\ \rm \longrightarrow ex = \dfrac{2e - 1}{e} \\ \\ \rm Divide \: both \: sides \: by \: e: \\ \rm \longrightarrow \dfrac{ex}{e} = \dfrac{2e - 1}{e \times e} \\ \\ \rm \longrightarrow x = \dfrac{2e - 1}{ {e}^{2} } [/tex]
