Question

solve for q.\
-75q + 25q - 12q + 52q + 35 = -85\
q = \boxed{}

Explanation:

Step1: Combine like terms for \( q \)

First, we combine the coefficients of \( q \): \(-75 + 25 - 12 + 52\). Let's calculate that: \(-75 + 25 = -50\), then \(-50 - 12 = -62\), and \(-62 + 52 = -10\). So the equation becomes \(-10q + 35 = -85\).

Step2: Subtract 35 from both sides

Subtract 35 from each side to isolate the term with \( q \): \(-10q + 35 - 35 = -85 - 35\). This simplifies to \(-10q = -120\).

Step3: Divide both sides by -10

Divide both sides by \(-10\) to solve for \( q \): \(\frac{-10q}{-10} = \frac{-120}{-10}\). This gives \( q = 12 \).

Answer:

\( q = 12 \)