Question

directions: solve each equation. show all st\\1. 5(n + 4) - (n + 7) = -11

Explanation:

Step1: Expand the brackets

First, we expand \(1.5(n + 4)\) and distribute the negative sign in \(-(n + 7)\).
\(1.5(n + 4)=1.5n+6\) and \(-(n + 7)=-n - 7\).
So the equation becomes \(1.5n+6 - n - 7=-11\).

Step2: Combine like terms

Combine the \(n\) terms and the constant terms.
For the \(n\) terms: \(1.5n - n = 0.5n\).
For the constant terms: \(6 - 7=-1\).
The equation now is \(0.5n-1=-11\).

Step3: Solve for \(n\)

Add 1 to both sides of the equation:
\(0.5n-1 + 1=-11 + 1\)
\(0.5n=-10\)
Then divide both sides by \(0.5\) (or multiply by 2):
\(n=\frac{-10}{0.5}=-20\)

Answer:

\(n = - 20\)