Solve for q: -10 + 10q - 10 = 10 + 4q.

Step-by-step solution

1. 1

   Tidy each side before moving anything across. The left side has two separate constants, $-10$ and $-10$, sitting on either side of the variable term. Combining them first prevents the classic slip of moving only one of them:

   $-10-10+10q=-20+10q$

   so the equation is $-20+10q=10+4q$.

2. 2

   Collect the variable terms on the side with the bigger coefficient. Since $10>4$, subtract $4q$ from both sides so the remaining coefficient stays positive:

   $-20+6q=10$

   Choosing this direction avoids ever dividing by a negative number.

3. 3

   Move the constant across. Add $20$ to both sides:

   $6q=30$

4. 4

   Divide by the coefficient.

   $q=\frac{30}{6}=5$

5. 5

   Check both sides independently. Left: $-10+10(5)-10=-10+50-10=30$. Right: $10+4(5)=10+20=30$. The two agree, so $q=5$ is correct. Evaluating each side separately, rather than re-running the algebra, is what makes this a genuine check.