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More # Solve the following equation: $\dfrac{{5x - 7}}{{3x + 1}} = 1$. Verified
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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 $\dfrac{{5x - 7}}{{3x + 1}} = 1$
Taking the denominator to the R.H.S, we have
$5x - 7 = 1\left( {3x + 1} \right) \\ 5x - 7 = 3x + 1 \\$
Grouping the variable terms, we get
$5x - 3x = 1 + 7$
Taking the variable as common, we have
$\left( {5 - 3} \right)x = 1 + 7 \\ 2x = 8 \\$
Therefore, we have
$x = \dfrac{8}{2} = 4 \\ \therefore x = 4 \\$
Thus, the value of the variable $x$in equation $\dfrac{{5x - 7}}{{3x + 1}} = 1$is 4.

Note: This problem involves solving a linear equation in one variable with variables on both sides by taking the denominator to the right-hand side (R.H.S). The degree (highest power) of the linear equation is one. So, we have only one solution to the equation.
Last updated date: 26th May 2023
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