# How do you solve 3x + 19 = 3 - 5x?

Jun 24, 2018

$x = - 2$

#### Explanation:

$3 x + 19 = 3 - 5 x$

$\therefore 3 x + 5 x = 3 - 19$

$\therefore 8 x = - 16$

$\therefore x = - \frac{16}{8}$

$\therefore x = - 2$

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check:-

substitute $x = - 2$

$\therefore 3 \left(- 2\right) + 19 = 3 - 5 \left(- 2\right)$

$\therefore - 6 + 19 = 3 + 10$

$\therefore 13 = 13$

Jun 24, 2018

$x = - 2$

#### Explanation:

Given: $3 x + 19 = 3 - 5 x$

To end up with all the $x$ terms on the left sides add $\textcolor{red}{5 x}$ to both sides.

$\textcolor{g r e e n}{3 x + 19 = 3 - 5 x \textcolor{w h i t e}{\text{dddd") ->color(white)("dddd")ubrace(3xcolor(red)(+5x))color(white)("d") +19 = 3color(white)("d}} \underbrace{- 5 x \textcolor{red}{+ 5 x}}}$
$\textcolor{w h i t e}{\text{ddddddddddddddddddddddddd.d") darrcolor(white)("dddddddddddddd}} \downarrow$
$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{dddddddddddddddddd") ->color(white)("dddddd") 8xcolor(white)("ddd") +19 =3color(white)("...}} + 0}$

Subtract 19 from both sides $\to \textcolor{w h i t e}{\text{ddd}} 8 x = - 16$

Divide both sides by $\textcolor{red}{8}$

$\textcolor{g r e e n}{8 x = - 16 \textcolor{w h i t e}{\text{dddddddddd") ->color(white)("ddddd}} \frac{8}{\textcolor{red}{8}} x = - \frac{16}{\textcolor{red}{8}}}$

But $\frac{8}{8} = 1 \mathmr{and} 1 \times x = x$

$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{ddddddddddddddddddd") ->color(white)("dddddd}} x = - 2}$