# How do you solve 0.25( 4f - 3) = 0.05( 10f - 9)?

Jul 16, 2017

$f = 0.6$

#### Explanation:

$0.25 \left(\setminus \textcolor{b l u e}{4 f} \setminus \textcolor{red}{- 3}\right) = 0.05 \left(\setminus \textcolor{s e a g r e e n}{10 f} \setminus \textcolor{p a \le v i o \le t red}{- 9}\right)$

• distributive
$\setminus \Rightarrow 0.25 \left(\setminus \textcolor{b l u e}{4 f}\right) + 0.25 \left(\setminus \textcolor{red}{- 3}\right) = 0.05 \left(\setminus \textcolor{s e a g r e e n}{10 f}\right) - 0.05 \left(\setminus \textcolor{p a \le v i o \le t red}{- 9}\right)$
• simplify
$\setminus \Rightarrow \setminus \textcolor{b l u e}{1} f \setminus \textcolor{red}{- 0.75} = \setminus \textcolor{s e a g r e e n}{0.5 f} \setminus \textcolor{p a \le v i o \le t red}{- 0.45}$
$\setminus \Rightarrow \setminus \textcolor{\mathmr{and} a n \ge}{f} \setminus \textcolor{s k y b l u e}{- 0.75} = \setminus \textcolor{\mathmr{and} a n \ge}{0.5 f} \setminus \textcolor{s k y b l u e}{- 0.45}$
• combine like terms
$\setminus \Rightarrow \setminus \textcolor{\mathmr{and} a n \ge}{f - 0.5 f} = \setminus \textcolor{s k y b l u e}{0.75 - 0.45}$
$\setminus \Rightarrow \setminus \textcolor{\mathmr{and} a n \ge}{0.5 f} = \setminus \textcolor{s k y b l u e}{0.30}$
• get variable alone: $f = 0.30 \setminus \div 0.5 = 0.6$
$\setminus \therefore f = 0.6$