# t=t0+(frac{k}{2})w, for w

$t={t}_{0}+\left(\frac{k}{2}\right)w$, for w

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irwchh

We are given:
$t={t}_{0}+\left(\frac{k}{2}\right)w$
Subtract t0 from both sides:
$t-{t}_{0}={t}_{0}+\left(\frac{k}{2}\right)w-t0$
$t-{t}_{0}=\left(\frac{k}{2}\right)w$
Multiply both sides by $\frac{2}{k}$
$\left(t-{t}_{0}\right)\frac{2}{k}=\left(\frac{k}{2}\right)w\cdot \left(\frac{2}{k}\right)$
$\frac{2\left(t-{t}_{0}\right)}{k}=w$
$w=2\frac{t-{t}_{0}}{k}$