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Question

Solve each equation below. 5x+43=2x+15\frac{5 x+4}{3}=\frac{2 x+1}{5}

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The solution of the given algebraic equation is described below.

5x+43=2x+155(5x+4)=3(2x+1)25x+20=6x+325x+206x=6x+36x19x+20=319x+2020=32019x=1719x19=1719x=1719\begin{align*} \dfrac{5x+4}{3}&=\dfrac{2x+1}{5}\tag{find the cross product}\\ 5(5x+4)&=3(2x+1)\\ 25x+20&=6x+3\tag{subtract $6x$ from both sides}\\ 25x+20-6x&=6x+3-6x\\ 19x+20&=3\tag{subtract $20$ from both sides}\\ 19x+20-20&=3-20\\ 19x&=-17\tag{divide both sides by $19$}\\ \dfrac{19x}{19}&=\dfrac{-17}{19}\\ x&=\dfrac{-17}{19} \end{align*}

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