# How do you solve 2+6x=7+7x?

Apr 21, 2018

$x = - 5$

#### Explanation:

$\text{collect terms in x on one side of the equation and}$
$\text{numeric values on the other side}$

$\text{subtract 7x from both sides}$

$2 + 6 x - 7 x = 7 \cancel{+ 7 x} \cancel{- 7 x}$

$\text{ subtracting 2 from both sides to get the numeric values}$
$\text{on one side}$

$\Rightarrow \cancel{2} - \cancel{2} - x = \left(7 - 2\right)$

$\Rightarrow - x = 5$

$\text{multiply both sides by } - 1$

$- 1 \times - x = - 1 \times 5$

$\Rightarrow x = - 5$

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

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

$\text{left } = 2 + \left(6 \times - 5\right) = 2 - 30 = - 28$

$\text{right } = 7 + \left(7 \times - 5\right) = 7 - 35 = - 28$

$\Rightarrow x = - 5 \text{ is the solution}$

Apr 21, 2018

$x = - 5$

#### Explanation:

Firstly, remember whatever we do to one side, we must do to the other.

Isolate $x$ to one side by subtracting $6 x$:

$2 + \cancel{6 x} = 7 + x$

Isolate $x$ again by cancelling out the constant $\left(7\right)$ by subtracting $7$:

$- 5 = \cancel{7} + x \to - 5 = x$