You have the following equation:
[tex]\frac{10}{2x+1}=\frac{14}{4x-7}[/tex]In order to solve for x the previous equation, multiply both sides by the LCM of the denominators, which is (2x+1)(4x-7):
[tex]\begin{gathered} (2x+1)(4x-7)\frac{10}{2x+1}=(2x+1)(4x-7)\frac{14}{4x-7} \\ (4x-7)10=(2x+1)14 \\ 40x-70=28x+14 \\ 40x-28x=14+70 \\ 12x=84 \\ x=\frac{84}{12} \\ x=7 \end{gathered}[/tex]Hence, the solution to the given equation is x = 7
