Simplifying Algebraic Expressions

1. Combine the \(n\) terms:

\(\begin{aligned}

-n+(-4)-(-4 n)+6 &=(-1+4) n-4+6 \\

&=3 n-4+6

\end{aligned}\)

Combine the numeric terms:

\(3 n-4+6=3 n+2\)

The simplified expression is \(3n + 2\).

2. Combine the \(x\) terms:

\(\begin{aligned}

-2 x-x+8 &=(-2-1) x+8 \\

&=-3 x+8

\end{aligned}\)

The simplified expression is \( -3x + 8 \).

3. Combine the \(s\) terms:

\(\begin{aligned}

2 s+(-4 s) &=(2-4) s \\

&=-2 s

\end{aligned}\)

The simplified expression is \(-2s\).

4. Combine the numeric terms:

\(-3 x-6-1=-3 x-7\)

The simplified expression is \(-3x - 7\).

5. Combine the \(r\) terms:

\(\begin{aligned}

2 r+1+(-4 r)+7 &=(2-4) r+1+7 \\

&=-2 r+1+7

\end{aligned}\)

Combine the numeric terms:

\(−2r+1+7=−2r+8\)

The simplified expression is \(-2r +8\).

6. Combine the \(r\) terms:

\( \begin{aligned}

-5 r+8 r+5 &=(-5+8) r+5 \\

&=3 r+5

\end{aligned}\)

The simplified expression is \(3r + 5\).

7. Combine the \(r\) terms:

\(\begin{aligned}

r+(-5 r) &=(1-5) r \\

&=-4 r

\end{aligned}\)

The simplified expression is \(-4r\).