# How do you solve for x in 2x+b=w?

Aug 2, 2016

$x = \frac{1}{2} \left(w - b\right)$

#### Explanation:

$\textcolor{red}{\text{Using first principles}}$

$\textcolor{red}{\text{Step 1}}$
Have only the terms with $x$ in them on the left of the =

Subtract $\textcolor{b l u e}{b}$ from both sides

$\textcolor{b r o w n}{2 x + b \text{ "=" "w" "->" "2x+bcolor(blue)(-b)" "=" } w \textcolor{b l u e}{- b}}$

$2 x + 0 = w - b$

$2 x = w - b$

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$\textcolor{red}{\text{Step 2}}$
Have only $x$ on the left hand side of the =

Divide both sides by $\textcolor{b l u e}{2}$

color(brown)(2/(color(blue)(2))xx x=color(blue)(1/2)(w-b)

$1 \times x = \frac{1}{2} \left(w - b\right)$

$x = \frac{1}{2} \left(w - b\right)$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{red}{\text{Comment}}$

$\frac{1}{2} \left(w - b\right)$ is the same as $\frac{w}{2} - \frac{b}{2}$