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

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Answer 1 · 2016-08-02T13:54:06

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

$Using first principles$ $color(red)("Using first principles")$

$Step 1$ $color(red)("Step 1")$
Have only the terms with $x$ $x$ in them on the left of the =

Subtract $b$ $color(blue)(b)$ from both sides

$2 x + b = w \to 2 x + b - b = w - b$ $color(brown)(2x+b" "=" "w" "->" "2x+bcolor(blue)(-b)" "=" "w color(blue)(-b))$

$2 x + 0 = w - b$ $2x+0=w-b$

$2 x = w - b$ $2x=w-b$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$Step 2$ $color(red)("Step 2")$
Have only $x$ $x$ on the left hand side of the =

Divide both sides by $2$ $color(blue)(2)$

$\frac{2}{2} \times x = \frac{1}{2} (w - b)$ $color(brown)(2/(color(blue)(2))xx x=color(blue)(1/2)(w-b)$

$1 \times x = \frac{1}{2} (w - b)$ $1xx x=1/2(w-b)$

$x = \frac{1}{2} (w - b)$ $x=1/2(w-b)$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$Comment$ $color(red)("Comment")$

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

How do you solve for xxx in 2x+b=w2x+b=w2x+b=w?