Question

solve for q.
\\(\frac{2}{2q + 3} = \frac{1}{8}\\)
q = \boxed{}

Explanation:

Step1: Cross - multiply the equation

Given the equation \(\frac{2}{2q + 3}=\frac{1}{8}\), cross - multiplying (which is based on the property that if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\)) gives us \(2\times8 = 1\times(2q + 3)\).

Step2: Simplify both sides

Simplify the left - hand side: \(2\times8=16\), and the right - hand side remains \(2q + 3\). So our equation becomes \(16=2q + 3\).

Step3: Subtract 3 from both sides

Subtract 3 from both sides of the equation \(16 = 2q+3\). We get \(16 - 3=2q+3 - 3\), which simplifies to \(13 = 2q\).

Step4: Divide both sides by 2

Divide both sides of the equation \(13 = 2q\) by 2. So \(q=\frac{13}{2}=6.5\).

Answer:

\(q = \frac{13}{2}\) (or \(q = 6.5\))