Question

S= 2bh+2bw+2hw solve for w

Answer 1

$Solution, solve\:for\:w,\:s=2bh+2bw+2hw\quad :\quad w=\frac{s-2bh}{2\left(b+h\right)};\quad \:2\left(b+h\right)\ne \:0$

$Steps:$

$s=2bh+2bw+2hw$

$\mathrm{Switch\:sides},\\2bh+2bw+2hw=s$

$\mathrm{Subtract\:}2bh\mathrm{\:from\:both\:sides},\\2bh+2bw+2hw-2bh=s-2bh$

$Simplify,\\2bw+2hw=s-2bh$

$\mathrm{Factor}\:2bw+2hw,\\\mathrm{Rewrite\:as},\\2bw+2hw,\\\mathrm{Factor\:out\:common\:term\:}2w,\\2w\left(b+h\right),\\2w\left(b+h\right)=s-2bh$

$\mathrm{Divide\:both\:sides\:by\:}2\left(b+h\right);\quad \:2\left(b+h\right)\ne \:0,\\\frac{2w\left(b+h\right)}{2\left(b+h\right)}=\frac{s}{2\left(b+h\right)}-\frac{2bh}{2\left(b+h\right)};\quad \:2\left(b+h\right)\ne \:0$

$\mathrm{Simplify},\\w=\frac{s-2bh}{2\left(b+h\right)};\quad \:2\left(b+h\right)\ne \:0$

$\mathrm{The\:Correct\:Answer\:is\:w=\frac{s-2bh}{2\left(b+h\right)};\quad \:2\left(b+h\right)\ne \:0}$

$\mathrm{Hope\:This\:Helps!!!}$

$\mathrm{-Austint1414}$