How do you solve (x+1)/3 = (2x-1)/4?

Jun 21, 2018

$x = \frac{7}{2}$

Explanation:

$\text{multiply both sides by the lowest common multiple of}$
$\text{3 and 4 that is 12}$

${\cancel{12}}^{4} \times \frac{x + 1}{\cancel{3}} ^ 1 = {\cancel{12}}^{3} \times \frac{2 x - 1}{\cancel{4}} ^ 1$

$4 \left(x + 1\right) = 3 \left(2 x - 1\right) \leftarrow \textcolor{b l u e}{\text{distribute}}$

$4 x + 4 = 6 x - 3$

$\text{subtract "4x" from both sides}$

$4 = 2 x - 3$

$\text{add 3 to both sides and divide by 2}$

$7 = 2 x \Rightarrow x = \frac{7}{2}$

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

$\text{left } = \frac{\frac{7}{2} + \frac{2}{2}}{3} = \frac{\frac{9}{2}}{3} = \frac{9}{6} = \frac{3}{2}$

$\text{right } = \frac{\frac{14}{2} - \frac{2}{2}}{4} = \frac{6}{4} = \frac{3}{2}$

$x = \frac{7}{2} \text{ is the solution}$

Jun 21, 2018

$x = \frac{7}{2}$

Explanation:

Multiply both sides by $12$:

${\cancel{12}}^{4} \setminus \frac{x + 1}{\cancel{3}} = \setminus \frac{2 x - 1}{\cancel{4}} {\cancel{12}}^{3}$

So, the equation becomes

$4 \left(x + 1\right) = 3 \left(2 x - 1\right)$

Expand both sides to get

$4 x + 4 = 6 x - 3$

Subtract $6 x$ to both sides:

$- 2 x + 4 = - 3$

Subtract $4$ from both sides:

$- 2 x = - 7$

Divide both sides by $- 2$:

$x = \frac{7}{2}$