Final answer:
To solve the equation 2(12q+1) = -3(2q-1) + 8q + 4, we expand and simplify both sides, isolate the variable q, and then solve for q. After simplifying, we find that q = 5/22. We check the solution by substituting back into the original equation and confirming both sides equal.
Step-by-step explanation:
To solve the equation 2(12q+1) = -3(2q-1) + 8q + 4, we start by expanding both sides:
24q + 2 = -6q + 3 + 8q + 4.
Then, we combine like terms:
24q + 2 = 2q + 7.
Next, we move all the q terms to one side and the constant terms to the other side by subtracting 2q and 2 from both sides:
22q = 5.
Divide both sides by 22 to isolate q:
q = 5/22.
Finally, we check the solution by substituting q back into the original equation:
2(12(5/22)+1) ? -3(2(5/22)-1) + 8(5/22) + 4. Simplify to confirm if both sides are equal. In this case, they are, confirming the solution q = 5/22.
We eliminated terms wherever possible to simplify the algebra and checked the answer to ensure it is reasonable.