# How do you solve 2 + 11b = 8b + 15?

May 1, 2017

$b = \frac{13}{3}$

#### Explanation:

Collect terms in x on the left side of the equation and numeric values on the right side.

$\text{subtract 8b from both sides}$

$2 + 11 b - 8 b = \cancel{8 b} \cancel{- 8 b} + 15$

$\Rightarrow 2 + 3 b = 15$

$\text{subtract 2 from both sides}$

$\cancel{2} \cancel{- 2} + 3 b = 15 - 2$

$\Rightarrow 3 b = 13$

$\text{divide both sides by 3}$

$\frac{\cancel{3} b}{\cancel{3}} = \frac{13}{3}$

$\Rightarrow b = \frac{13}{3}$

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

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

$\text{left side } = 2 + \left(11 \times \frac{13}{3}\right) = \frac{6}{3} + \frac{143}{3} = \frac{149}{3}$

$\text{right side } = \left(8 \times \frac{13}{3}\right) + 15 = \frac{104}{3} + \frac{45}{3} = \frac{149}{3}$

$\Rightarrow b = \frac{13}{3} \text{ is the solution}$