To solve for [tex]\( y \)[/tex] in the equation
[tex]\[ a \cdot (n + y) = 10y + 32, \][/tex]
we need to isolate [tex]\( y \)[/tex]. Follow these steps:
1. Distribute [tex]\( a \)[/tex] on the left-hand side of the equation:
[tex]\[ a \cdot n + a \cdot y = 10y + 32. \][/tex]
2. Move all the terms involving [tex]\( y \)[/tex] to one side of the equation:
[tex]\[ a \cdot n + a \cdot y - 10y = 32. \][/tex]
This can be simplified to:
[tex]\[ a \cdot y - 10y = 32 - a \cdot n. \][/tex]
3. Factor out [tex]\( y \)[/tex] from the left-hand side:
[tex]\[ y(a - 10) = 32 - a \cdot n. \][/tex]
4. Solve for [tex]\( y \)[/tex] by dividing both sides by [tex]\( a - 10 \)[/tex]:
[tex]\[ y = \frac{32 - a \cdot n}{a - 10}. \][/tex]
Thus, the solution for [tex]\( y \)[/tex] is:
[tex]\[ y = \frac{32 - a \cdot n}{a - 10}. \][/tex]
