Let's solve the given equation step by step to express [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex].
The given equation is:
[tex]\[ 6x + y = 4x + 11y \][/tex]
First, we want to gather all the terms involving [tex]\( y \)[/tex] on one side of the equation and all the terms involving [tex]\( x \)[/tex] on the other side:
1. Subtract [tex]\( 4x \)[/tex] from both sides of the equation:
[tex]\[ 6x + y - 4x = 4x + 11y - 4x \][/tex]
Simplifying, we get:
[tex]\[ 2x + y = 11y \][/tex]
2. Subtract [tex]\( y \)[/tex] from both sides of the equation:
[tex]\[ 2x + y - y = 11y - y \][/tex]
Simplifying, we get:
[tex]\[ 2x = 10y \][/tex]
3. Finally, we need to solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]. To do this, divide both sides of the equation by 10:
[tex]\[ \frac{2x}{10} = \frac{10y}{10} \][/tex]
Simplifying, we get:
[tex]\[ \frac{x}{5} = y \][/tex]
So, we have expressed [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex] as:
[tex]\[ y = \frac{x}{5} \][/tex]
Therefore, the rearranged equation is:
[tex]\[ y = \frac{x}{5} \][/tex]
