# How do you solve 2(f-3) + 5 = 3(f-1)?

Jun 17, 2018

$\textcolor{b l u e}{f = 2}$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} 2 \left(f - 3\right) + 5 = 3 \left(f - 1\right)$

Simplifying each side:
$L . S .$
$\textcolor{w h i t e}{\text{XXX}} = 2 \left(f - 3\right) + 5$
$\textcolor{w h i t e}{\text{XXX}} = 2 f - 6 + 5$
$\textcolor{w h i t e}{\text{XXX}} = 2 f - 1$
$R . S .$
$\textcolor{w h i t e}{\text{XXX}} = 3 \left(f - 1\right)$
$\textcolor{w h i t e}{\text{XXX}} = 3 f - 3$

Since $L . S . = R . S .$
$\textcolor{w h i t e}{\text{XXX}} 2 f - 1 = 3 f - 3$

Subtracting $2 f$ from both sides
$\textcolor{w h i t e}{\text{XXX}} - 1 = f - 3$
then adding $3$ to both sides
color(white)("XXX")2=fcolor(white)("xxxxxxxx")" or, if you prefer: "f=2