We want to solve the equation
[tex]\text{ -6\lparen -4v+1\rparen -v=7\lparen v -3\rparen -3}[/tex]
we start by distributing on both sides the multiplication. So we get
[tex](\text{ -6\rparen\lparen -4\rparen v - 6 - v =}7v\text{ - 3}\cdot7\text{ -3}[/tex]
if we operate, we get
[tex]24v\text{ -6 -v=7v - 21 -3}[/tex]
if we operate on both sides, we get
[tex]23v\text{ -6=7v - 24}[/tex]
we start by subtracting 7v on both sides, so we get
[tex]\begin{gathered} 23v\text{ -6 - 7v= -24} \\ 16v\text{ -6= -24} \end{gathered}[/tex]
now, we add 6 on both sides. So we get
[tex]16v=\text{ -}24+6=\text{ -18}[/tex]
so if we divide both sides by 16 we get
[tex]v=\text{ - }\frac{18}{16}=\text{ -}\frac{9\cdot2}{8\cdot2}=\text{ -}\frac{9}{8}[/tex]
so the value of v is -9/8
