How do you solve 4( b + 6) = 2( b + 5) + 2?

Jun 5, 2018

$b = - 6$

Explanation:

$4 \left(b + 6\right) = 2 \left(b + 5\right) + 2$

To solve for the variable $b$, we need to make it by itself. First, use the distributive property (shown below) to simplify $4 \left(b + 6\right)$ and $2 \left(b + 5\right)$:

Following this image, we know that:
$\textcolor{b l u e}{4 \left(b + 6\right) = \left(4 \cdot b\right) + \left(4 \cdot 6\right) = 4 b + 24}$
and
$\textcolor{b l u e}{2 \left(b + 5\right) = \left(2 \cdot b\right) + \left(2 \cdot 5\right) = 2 b + 10}$

Put them back into the equation:
$4 b + 24 = 2 b + 10 + 2$

Combine $10 + 2$:
$4 b + 24 = 2 b + 12$

Subtract $\textcolor{b l u e}{2 b}$ from both sides:
$4 b + 24 \quad \textcolor{b l u e}{- \quad 2 b} = 2 b + 12 \quad \textcolor{b l u e}{- \quad 2 b}$

$2 b + 24 = 12$

Now subtract $\textcolor{b l u e}{24}$ from both sides:
$2 b + 24 \quad \textcolor{b l u e}{- \quad 24} = 12 \quad \textcolor{b l u e}{- \quad 24}$

$2 b = - 12$

Divide both sides by $\textcolor{b l u e}{2}$:
$\frac{2 b}{\textcolor{b l u e}{2}} = - \frac{12}{\textcolor{b l u e}{2}}$

Therefore,
$b = - 6$

Hope this helps!