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

May 30, 2018

$x = - 1$

Explanation:

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

First, use the distributive property to simplify $2 \left(x - 1\right)$ and $- 3 \left(x + 1\right)$:

Following this image, we know that:
$\textcolor{b l u e}{2 \left(x - 1\right) = \left(2 \cdot x\right) + \left(2 \cdot - 1\right) = 2 x - 1}$
and
$\textcolor{b l u e}{- 3 \left(x + 1\right) = \left(- 3 \cdot x\right) + \left(- 3 \cdot 1\right) = - 3 x + - 3}$

Put them back into the equation:
$2 x - 2 + 3 = x - 3 x - 3$

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

Add $\textcolor{b l u e}{2 x}$ to both sides of the equation:
$2 x + 1 \quad \textcolor{b l u e}{+ \quad 2 x} = - 2 x - 3 \quad \textcolor{b l u e}{+ \quad 2 x}$

$4 x + 1 = - 3$

Subtract $\textcolor{b l u e}{1}$ from both sides of the equation:
$4 x + 1 \quad \textcolor{b l u e}{- \quad 1} = - 3 \quad \textcolor{b l u e}{- \quad 1}$

$4 x = - 4$

Divide both sides by $\textcolor{b l u e}{4}$:
$\frac{4 x}{\textcolor{b l u e}{4}} = - \frac{4}{\textcolor{b l u e}{4}}$

Therefore,
$x = - 1$

Hope this helps!