Question

solve for q.\\(\frac{3}{2}q + 4 - \frac{1}{3}q = -\frac{5}{6}q\\)\\(q =\\)

Explanation:

Step1: Combine like terms on the left

First, we combine the \(q\)-terms on the left side. The coefficients of \(q\) are \(\frac{3}{2}\) and \(-\frac{1}{3}\). To combine them, we find a common denominator, which is 6. So \(\frac{3}{2}q-\frac{1}{3}q=\frac{9}{6}q - \frac{2}{6}q=\frac{7}{6}q\). The equation becomes \(\frac{7}{6}q + 4=-\frac{5}{6}q\).

Step2: Add \(\frac{5}{6}q\) to both sides

Adding \(\frac{5}{6}q\) to both sides to get all \(q\)-terms on the left. \(\frac{7}{6}q+\frac{5}{6}q + 4=-\frac{5}{6}q+\frac{5}{6}q\). Combining the \(q\)-terms: \(\frac{12}{6}q+4 = 0\), which simplifies to \(2q+4 = 0\).

Step3: Subtract 4 from both sides

Subtract 4 from both sides: \(2q+4 - 4=0 - 4\), so \(2q=-4\).

Step4: Divide by 2

Divide both sides by 2: \(\frac{2q}{2}=\frac{-4}{2}\), so \(q = - 2\).

Answer:

\(-2\)