Question

# Solve the following equation: $\dfrac{{5x - 7}}{{3x + 1}} = 1$.

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Hint: If we solve the given equation it converts into a linear equation in one variable. In the given equation the variable is $x$. Since it is a linear equation in one variable, if we solve the equation, we will get one only one solution for the variable $x$. So, use this concept to reach the solution of the problem.

Given equation is $\dfrac{{5x - 7}}{{3x + 1}} = 1$
$5x - 7 = 1\left( {3x + 1} \right) \\ 5x - 7 = 3x + 1 \\$
$5x - 3x = 1 + 7$
$\left( {5 - 3} \right)x = 1 + 7 \\ 2x = 8 \\$
$x = \dfrac{8}{2} = 4 \\ \therefore x = 4 \\$
Thus, the value of the variable $x$in equation $\dfrac{{5x - 7}}{{3x + 1}} = 1$is 4.