1. Solve $d = rt$ for $r$. Start with the equation: $$d = rt$$ Divide both sides by $t$ to isolate $r$: $$r = \frac{d}{t}$$ 2. Solve $6w - y = 2z$ for $w$. Add $y$ to both sides: $$6w = 2z + y$$ Divide by 6: $$w = \frac{2z + y}{6}$$ 3. Solve $mx + 4y = 3t$ for $x$. Subtract $4y$: $$mx = 3t - 4y$$ Divide by $m$: $$x = \frac{3t - 4y}{m}$$ 4. Solve $9s - 5g = -4u$ for $s$. Add $5g$: $$9s = 5g - 4u$$ Divide by 9: $$s = \frac{5g - 4u}{9}$$ 5. Solve $db + 3c = 2x$ for $b$. Subtract $3c$: $$db = 2x - 3c$$ Divide by $d$: $$b = \frac{2x - 3c}{d}$$ 6. Solve $2p = kx - t$ for $x$. Add $t$ to both sides: $$2p + t = kx$$ Divide by $k$: $$x = \frac{2p + t}{k}$$ 7. Solve $\frac{2}{3}m + a = a + t$ for $m$. Subtract $a$: $$\frac{2}{3}m = t$$ Multiply both sides by $\frac{3}{2}$: $$m = \frac{3}{2}t$$ 8. Solve $\frac{2}{5}h + g = d$ for $h$. Subtract $g$: $$\frac{2}{5}h = d - g$$ Multiply both sides by $\frac{5}{2}$: $$h = \frac{5}{2}(d - g)$$ 9. Solve $\frac{2}{3}y + v = x$ for $y$. Subtract $v$: $$\frac{2}{3}y = x - v$$ Multiply both sides by $\frac{3}{2}$: $$y = \frac{3}{2}(x - v)$$ 10. Solve $\frac{3}{4}q - q = k$ for $q$. Rewrite: $$\frac{3}{4}q - 1q = k$$ Combine like terms: $$\left(\frac{3}{4} - 1\right)q = k$$ $$-\frac{1}{4}q = k$$ Multiply both sides by $-4$: $$q = -4k$$ 11. Solve $\frac{7x+9}{5} = h$ for $x$. Multiply both sides by 5: $$7x + 9 = 5h$$ Subtract 9: $$7x = 5h - 9$$ Divide by 7: $$x = \frac{5h - 9}{7}$$ 12. Solve $\frac{3b - 4}{2} = c$ for $b$. Multiply both sides by 2: $$3b - 4 = 2c$$ Add 4: $$3b = 2c + 4$$ Divide by 3: $$b = \frac{2c + 4}{3}$$ 13. Solve $2w - y = 7w - 2$ for $w$. Bring $w$ terms to one side: $$2w - 7w = -2 + y$$ $$-5w = y - 2$$ Divide by $-5$: $$w = \frac{2 - y}{5}$$ 14. Solve $3\ell + y = 5 + 5\ell$ for $\ell$. Bring $\ell$ terms together: $$3\ell - 5\ell = 5 - y$$ $$-2\ell = 5 - y$$ Divide by $-2$: $$\ell = \frac{y - 5}{2}$$ Final answers: