[tex] \large \bf \rm{ \color{yellow}A) \: 7(x - 5) = 3(x + 1)}[/tex]

[tex] \bf \rm{7x - 35 = 3(x + 1)} \\ \bf \rm7x - 35 = 3x + 3 \: \: \: [/tex]

[tex] \bf \rm{7x - 35 - 3x = 3} \\ \bf \rm{7x - 3x = 3 + 35}[/tex]

[tex] \bf \rm{4x = 3 + 35} \\ \bf \rm{4x = 38} \: \: \: \: \: \: \: [/tex]

[tex] \bf \rm{ \color{blue}\boxed{\boxed{\boxed{\color{lightblue}\large{x = \frac{19}{2}}}}} }\\ [/tex]

[tex] \bf \rm{ \color{yellow}{{B) \: 3(x - 2) = 4( - x + 3)}}}[/tex]

[tex] \bf{3x - 6 = 4( - x + 3)} \\ \bf{3x - 6 = - 4x + 12}[/tex]

[tex] \bf{3x - 6 + 4x = 12} \\ \bf{3x + 4x = 12 + 6}[/tex]

[tex] \bf{7x = 12 + 6} \\ \bf{7x = 18} \: \: \: \: \: \: \: \: [/tex]

[tex] \bf \rm{ \color{blue}{{\boxed{\boxed{\boxed{{\color{lightblue}x = \frac{18}{7}}}} }}} }[/tex]

[tex] \bf \rm{ \color{yellow}{C) \: 2(x + 1) - (x - 1) = 0}}[/tex]

[tex] \rm{2x + 2 - (x - 1) = 0} \\ \rm{2x + 2 - x + 1 = 0} \: \: \: [/tex]

[tex] \rm{x + 2 + 1 = 0} \\ \rm{x + 3 = 0} \: \: \: \: \: \: \: [/tex]

[tex] \bf \rm{ \color{blue}\boxed{ \boxed{\boxed{\color{lightblue}x = - 3}}}}[/tex]

[tex] \bf \rm{ \color{yellow}{ D) \: 5(x + 1) - 3(x + 2) = 0 }}[/tex]

[tex] \rm{5x + 5 - 3(x + 2) = 0} \\ \rm{5x + 5 - 3x - 6 = 0}[/tex]

[tex] \rm{2x + 5 - 6 = 0} \\ \rm{2x - 1 = 0} \: \: \: \: \: \: \: [/tex]

[tex] \rm{2x = 1} [/tex]

[tex] \bf \rm{ \color{blue}\boxed{ \boxed{\boxed{\color{lightblue}x = \frac{1}{2} }}}}[/tex]