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 $-4r$.