Question

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

Explanation:

Step1: Simplify both sides

Left side: \(3(q - 4)+2q = 3q - 12 + 2q = 5q - 12\)
Right side: \(q - 8 + 6(q + 2)=q - 8 + 6q + 12 = 7q + 4\)

Step2: Solve for \(q\)

Set the simplified left and right sides equal: \(5q - 12 = 7q + 4\)
Subtract \(5q\) from both sides: \(-12 = 2q + 4\)
Subtract \(4\) from both sides: \(-16 = 2q\)
Divide both sides by \(2\): \(q = -8\)

Answer:

\(q = -8\)