How do you solve 6 (x + 1) - 5 = x + 31?

Apr 28, 2017

$x = 6$

Explanation:

$\text{ the first step is to distribute the bracket}$

$6 x + 6 - 5 = x + 31$

$\text{simplifying left side}$

$6 x + 1 = x + 31$

$\text{subtract x from both sides}$

$6 x - x + 1 = \cancel{x} \cancel{- x} + 31$

$\Rightarrow 5 x + 1 = 31$

$\text{subtract 1 from both sides}$

$5 x \cancel{+ 1} \cancel{- 1} = 31 - 1$

$\Rightarrow 5 x = 30$

$\text{divide both sides by 5}$

$\frac{\cancel{5} x}{\cancel{5}} = \frac{30}{5}$

$\Rightarrow x = 6$

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

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

$\text{left side } = 6 \left(6 + 1\right) - 5 = 42 - 5 = 37$

$\text{right side } = 6 + 31 = 37$

$\Rightarrow x = 6 \text{ is the solution}$