Question

Solve for v.-6(-4v+1)-v=7(v-3)-3 Simplify your answer as much as possible!

Answer 1

We want to solve the equation

$\text{ -6\lparen -4v+1\rparen -v=7\lparen v -3\rparen -3}$

we start by distributing on both sides the multiplication. So we get

$(\text{ -6\rparen\lparen -4\rparen v - 6 - v =}7v\text{ - 3}\cdot7\text{ -3}$

if we operate, we get

$24v\text{ -6 -v=7v - 21 -3}$

if we operate on both sides, we get

$23v\text{ -6=7v - 24}$

we start by subtracting 7v on both sides, so we get

$\begin{gathered} 23v\text{ -6 - 7v= -24} \\ 16v\text{ -6= -24} \end{gathered}$

now, we add 6 on both sides. So we get

$16v=\text{ -}24+6=\text{ -18}$

so if we divide both sides by 16 we get

$v=\text{ - }\frac{18}{16}=\text{ -}\frac{9\cdot2}{8\cdot2}=\text{ -}\frac{9}{8}$

so the value of v is -9/8