Question

$\frac{3x+5}{4x+2}=\frac{3x+4}{4x+7}.$ Solve this linear equation.

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Solution

Solving the equation:We have,$\frac{3x+5}{4x+2}=\frac{3x+4}{4x+7}$By cross-multiplying we get$\left(3x+5\right)\left(4x+7\right)=\left(3x+4\right)\left(4x+2\right)$Now applying the distributive property.$\begin{array}{rcl}3x\left(4x+7\right)+5\left(4x+7\right)& =& 3x\left(4x+2\right)+4\left(4x+2\right)\\ \overline{)12{x}^{2}}+21x+20x+35& =& \overline{)12{x}^{2}}+6x+16x+8\\ 41x+35& =& 22x+8\\ 19x& =& -27\\ x& =& -\frac{27}{19}\end{array}$Hence, the solution of the linear equation is $\begin{array}{rcl}& & -\frac{27}{19}\end{array}$

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