Final answer:
To solve the equation 8q + 4q + 4 = 4q - 8, combine like terms, manipulate to isolate the variable 'q', and divide by the coefficient to find the solution q = -1.5.
Step-by-step explanation:
To solve the equation 8q + 4q + 4 = 4q - 8, we first combine like terms on the left side of the equation. The terms involving 'q' can be added together:
8q + 4q = 12q
So, the equation simplifies to:
12q + 4 = 4q - 8
Next, we want all the terms involving 'q' on one side and all the constant terms on the other. To do this, we subtract 4q from both sides:
12q - 4q + 4 = 4q - 4q - 8
This simplifies to:
8q + 4 = -8
Now, we subtract 4 from both sides to solve for 'q':
8q = -8 - 4
8q = -12
Finally, we divide both sides by 8 to isolate 'q':
q = -12 / 8
q = -1.5
The solution to the equation is q = -1.5.