# What is the value of x? (thanks!)

## 2x+2=3x-63

Nov 27, 2017

$x = 65$

#### Explanation:

$2 x + 2 = 3 x - 63$

Firstly, we can subtract $2 x$ from both sides of the equation:

$2 x + 2 - 2 x = 3 x - 63 - 2 x$

Which gives:

$2 = x - 63$

We can then add $63$ to both sides also:

$2 + 63 = x - 63 + 63$

Which gives:

$65 = x$

Nov 27, 2017

$x = 65$

#### Explanation:

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

$\text{subtract 2x from both sides}$

$\cancel{2 x} \cancel{- 2 x} + 2 = 3 x - 2 x - 63$

$\Rightarrow 2 = x - 63$

$\text{add 63 to both sides}$

$2 + 63 = x \cancel{- 63} \cancel{+ 63}$

$\Rightarrow 65 = x \to x = 65$

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

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

$\text{left } = \left(2 \times 65\right) + 2 = 130 + 2 = 132$

$\text{right } = \left(3 \times 65\right) - 63 = 195 - 63 = 132$

$\Rightarrow x = 65 \text{ is the solution}$