# How do you solve (3x-1)/(5x+4 )= 4?

Mar 28, 2018

$x = - 1$

#### Explanation:

$\text{to eliminate the fraction multiply both sides by } 5 x + 4$

$\cancel{5 x + 4} \times \frac{3 x - 1}{\cancel{5 x + 4}} = 4 \left(5 x + 4\right)$

$\Rightarrow 3 x - 1 = 4 \left(5 x + 4\right) \leftarrow \textcolor{b l u e}{\text{distribute}}$

$\Rightarrow 3 x - 1 = 20 x + 16$

$\text{subtract "20x" from both sides}$

$3 x - 20 x - 1 = \cancel{20 x} \cancel{- 20 x} + 16$

$\Rightarrow - 17 x - 1 = 16$

$\text{add 1 to both sides}$

$- 17 x \cancel{- 1} \cancel{+ 1} = 16 + 1$

$\Rightarrow - 17 x = 17$

$\text{divide both sides by } - 17$

$\frac{\cancel{- 17} x}{\cancel{- 17}} = \frac{- 17}{17}$

$\Rightarrow x = - 1$

$\textcolor{b l u e}{\text{As a check}}$

Substitute this value into the left side of the equation and if equal to the right side then it is the solution.

$\frac{- 3 - 1}{- 5 + 4} = \frac{- 4}{- 1} = 4 = \text{ right side}$

$\Rightarrow x = - 1 \text{ is the solution}$

Mar 28, 2018

$\left(5 x + 4\right) \cdot \frac{3 x - 1}{5 x + 4} = 4 \cdot \left(5 x + 4\right)$
therefore $3 x - 1 = 20 x + 16$
$- 16 - 1 = 20 x - 3 x$
$- \frac{17}{17} = 17 \frac{x}{17}$ therefore $x = - 1$
you firstly dissolve the denominator on the left side by multiplying with $5 x + 4$ both sides. Then collect like terms, the once with the variable $x$ on one side and one with real numbers on the other side. then solve to get the answer.