Answer: \(x=\frac{13}{14}\) or \(x=-\frac{1}{14}\).

Answer: \(x=\frac{13}{14}\) or \(x=-\frac{1}{14}\).

Start by isolating the modulus term:

\(4|7x-3|-5=9\)

\(4|7x-3|=14\)

\(|7x-3|=\frac72\).

So either

\(7x-3=\frac72\quad\text{or}\quad 7x-3=-\frac72\).

From the first equation, \(7x=\frac{13}{2}\), so \(x=\frac{13}{14}\).

From the second equation, \(7x=-\frac12\), so \(x=-\frac{1}{14}\).