l) $$ \frac{5}{3}(e-6)=\frac{e}{7}+22 $$

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解方程 $$ \frac{5}{3}(e-6)=\frac{e}{7}+22 $$
Solve the equation by following steps:
- step0: Solve for $$e$$:
  $$\frac{5}{3}\left(e-6ight)=\frac{e}{7}+22$$
- step1: Multiply the terms:
  $$\frac{5}{3}e-10=\frac{e}{7}+22$$
- step2: Multiply both sides of the equation by LCD:
  $$\left(\frac{5}{3}e-10ight)	imes 21=\left(\frac{e}{7}+22ight)	imes 21$$
- step3: Simplify the equation:
  $$35e-210=3e+462$$
- step4: Move the expression to the left side:
  $$35e-3e=462+210$$
- step5: Add and subtract:
  $$32e=462+210$$
- step6: Add and subtract:
  $$32e=672$$
- step7: Divide both sides:
  $$\frac{32e}{32}=\frac{672}{32}$$
- step8: Divide the numbers:
  $$e=21$$
解方程 $$ \frac{5}{3}(e-6)=\frac{e}{7}+22 $$ 后得到 $$ e=21 $$。
$$ e=21 $$

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