# How do you solve for x: 5(x-3)+2(3-x)=12?

Jun 22, 2016

You first work away the parentheses

#### Explanation:

$\to \left(5 \cdot x - 5 \cdot 3\right) + \left(2 \cdot 3 - 2 \cdot x\right) = 12$
(these brackets only used for clarification)

$\to 5 x - 15 + 6 - 2 x = 12 \to 3 x - 9 = 12$

Add $9$ to both sides:
$\to 3 x - \cancel{9} + \cancel{9} = 12 + 9$
$\to 3 x = 21 \to x = 7$

Jun 22, 2016

Just a different approach

$x = 7$

#### Explanation:

Given:$\text{ } 5 \left(x - 3\right) + 2 \left(3 - x\right) = 12$

If we can change $2 \left(3 - x\right) \text{ such that "(3-x)" became } \left(x - 3\right)$ then we have a common factor.

Note that
$- 2 \left(x - 3\right) = - 2 x + 6 \text{ "->" } + 2 \left(3 - x\right) = - 2 x + 6$

Write the given equation as:

$5 \left(x - 3\right) - 2 \left(x - 3\right) = 12$

Factor out $\left(x - 3\right)$

$\left(x - 3\right) \left(5 - 2\right) = 12$

$3 \left(x - 3\right) = 12$

Divide both sides by 3

$x - 3 = 4$

$x = 7$