i need help

Zora is budgeting her available time for the next couple days. She spent 2 over 5 of her time on homework and then 3 over 10 of her time on the internet. Homework and time on the internet consumed 14 hours. How much available time did Zora have to budget

x = budget

\(\begin{array}{rcll} \dfrac{2}{5}\cdot x + \dfrac{3}{10} \cdot x &=& 14\ h \\ x\cdot \left( \dfrac{2}{5} + \dfrac{3}{10} \right) &=& 14\ h \\ x\cdot \left( \dfrac{2\cdot 10+5\cdot 3}{5\cdot 10} \right) &=& 14\ h \\ x\cdot \left( \dfrac{20+15}{50} \right) &=& 14\ h \\ x\cdot \dfrac{35}{50} &=& 14\ h \\ x\cdot \dfrac{5\cdot 7}{5\cdot 10} &=& 14\ h \\ x\cdot \dfrac{ 7 }{ 10 } &=& 14\ h \quad & | \quad \cdot \dfrac{ 10 }{ 7 } \\ x &=& \dfrac{ 10 }{ 7 }\cdot 14\ h \\ x &=& 10\cdot 2\ h \\ \mathbf{ x }& \mathbf{=} & \mathbf{ 20\ h } \\ \end{array}\)

\(\begin{array}{rcll} 20\ h \cdot \dfrac{2}{5} &=& 8\ h \\\\ 20\ h \cdot \dfrac{3}{10} &=& 6\ h \\\\ 8\ h +6\ h &=&14\ h \end{array}\)

Zora has 20 hours