Question

Solve for X. Write down what type of solution the equation has. 3)
`(10)/(2x + 1) = (14)/(4x - 7)`

Answer 1

You have the following equation:

`(10)/(2x+1)=(14)/(4x-7)`

In order to solve for x the previous equation, multiply both sides by the LCM of the denominators, which is (2x+1)(4x-7):

`\begin{gathered} (2x+1)(4x-7)(10)/(2x+1)=(2x+1)(4x-7)(14)/(4x-7) \\ (4x-7)10=(2x+1)14 \\ 40x-70=28x+14 \\ 40x-28x=14+70 \\ 12x=84 \\ x=(84)/(12) \\ x=7 \end{gathered}`

Hence, the solution to the given equation is x = 7