Rewrite in simplest terms: -(-9q + 3r) + 6r - 2(-4r + 9q).

Step-by-step solution

1. 1

   Treat the leading minus as multiplication by $-1$. A bare minus in front of a bracket is the most common place to lose a sign, so make it explicit:

   $-(-9q+3r)=(-1)(-9q)+(-1)(3r)=9q-3r$

   Both signs inside flip — not just the first one.

2. 2

   Distribute the $-2$ over the second bracket. Again every term inside is affected:

   $-2(-4r+9q)=(-2)(-4r)+(-2)(9q)=8r-18q$

   The product of two negatives gives $+8r$, while $-2\cdot 9q$ gives $-18q$.

3. 3

   Rewrite the whole expression with no brackets left.

   $9q-3r+6r+8r-18q$

4. 4

   Collect like terms, one variable at a time. The $q$ terms:

   $9q-18q=-9q$

   The $r$ terms:

   $-3r+6r+8r=11r$

   so the expression simplifies to $-9q+11r$. Terms in $q$ and $r$ can never be merged with each other — they are unlike.

5. 5

   Check by substituting numbers. Take $q=1$, $r=2$. Original: $-(-9+6)+12-2(-8+9)=3+12-2=13$. Simplified: $-9(1)+11(2)=-9+22=13\;\checkmark$. A second test with $q=-1$, $r=0$ gives $-(9)+0-2(-9)=-9+18=9$ and $-9(-1)+0=9\;\checkmark$. Two independent values are enough to confirm a linear expression in two variables.