# How do you solve 4(u+1)+5=6(u-1)+u?

Apr 26, 2017

$u = 5$

#### Explanation:

Distribute brackets on both sides of the equation.

$4 u + 4 + 5 = 6 u - 6 + u$

$\text{simplify both sides}$

$4 u + 9 = 7 u - 6$

$\text{subtract 7u from both sides}$

$4 u - 7 u + 9 = \cancel{7 u} \cancel{- 7 u} - 6$

$\Rightarrow - 3 u + 9 = - 6$

$\text{subtract 9 from both sides}$

$- 3 u \cancel{+ 9} \cancel{- 9} = - 6 - 9$

$\Rightarrow - 3 u = - 15$

$\text{divide both sides by - 3}$

$\frac{\cancel{- 9} u}{\cancel{- 9}} = \frac{- 15}{- 3}$

$\Rightarrow u = 5$

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

Substitute this value into the equation and if both sides are equal then it is the solution.

$\text{left side } = 4 \left(5 + 1\right) + 5 = \left(4 \times 6\right) + 5 = 24 + 5 = 29$

$\text{right side } = 6 \left(5 - 1\right) + 5 = \left(6 \times 4\right) + 5 = 29$

$\Rightarrow u = 5 \text{ is the solution}$