Question

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

Answer 1

`f=0.6`

Explanation:

`0.25(\color(blue)(4f)\color(red)(-3))=0.05(\color(seagreen)(10f)\color(palevioletred)(-9))`

• distributive
  `\rArr0.25(\color(blue)(4f))+0.25(\color(red)(-3))=0.05(\color(seagreen)(10f))-0.05(\color(palevioletred)(-9))`
• simplify
  `\rArr\color(blue)(1)f\color(red)(-0.75)=\color(seagreen)(0.5f)\color(palevioletred)(-0.45)`
  `\rArr\color(orange)(f)\color(skyblue)(-0.75)=\color(orange)(0.5f)\color(skyblue)(-0.45)`
• combine like terms
  `\rArr\color(orange)(f-0.5f)=\color(skyblue)(0.75-0.45)`
  `\rArr\color(orange)(0.5f)=\color(skyblue)(0.30)`
• get variable alone: `f=0.30\div0.5=0.6`
  `\thereforef=0.6`