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

Mar 2, 2018

$x = - 1$

#### Explanation:

$\text{distribute brackets on both sides of the equation}$

$2 x - 2 + 3 = x - 3 x - 3$

$\text{simplify both sides}$

$2 x + 1 = - 2 x - 3$

$\text{add 2x to both sides}$

$2 x + 2 x + 1 = \cancel{- 2 x} \cancel{+ 2 x} - 3$

$\Rightarrow 4 x + 1 = - 3$

$\text{subtract 1 from both sides}$

$4 x \cancel{+ 1} \cancel{- 1} = - 3 - 1$

$\Rightarrow 4 x = - 4$

$\text{divide both sides by 4}$

$\frac{\cancel{4} x}{\cancel{4}} = \frac{- 4}{4}$

$\Rightarrow x = - 1$

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

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

$\text{left } = 2 \left(- 2\right) + 3 = - 4 + 3 = - 1$

$\text{right } = - 1 - 3 \left(0\right) = - 1$

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

Mar 2, 2018

$x = - 1$

#### Explanation:

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

Open the brackets from both the sides

$2 x - 2 + 3 = x - 3 x - 3$

Bring all $x$ terms on one side and the other terms on the other side

$2 x - x + 3 x = 2 - 3 - 3$

$4 x = - 4$

$x = \frac{- 4}{4}$

$x = - 1$