Question

3q - 12 + 2q = 4q - 8 + 6q + 12

Explanation:

Step1: Combine like terms on left side

Combine the \(q\)-terms: \(3q + 2q = 5q\), so left side is \(5q - 12\).

Step2: Combine like terms on right side

Combine the \(q\)-terms: \(9q+6q = 15q\), so right side is \(15q + 12\).

Step3: Move \(q\)-terms to one side

Subtract \(5q\) from both sides: \(5q - 12 - 5q=15q + 12 - 5q\), which simplifies to \(-12 = 10q+12\).

Step4: Isolate the \(q\)-term

Subtract 12 from both sides: \(-12 - 12=10q+12 - 12\), so \(-24 = 10q\).

Step5: Solve for \(q\)

Divide both sides by 10: \(q=\frac{-24}{10}=-\frac{12}{5}=-2.4\).

Answer:

\(q = -\frac{12}{5}\) (or \(q=-2.4\))