Answer: (a) \(x\gt \frac52\) or \(x\lt -2\); (b) \(x=\frac94\) or \(x=16\).

The key point is to split the absolute-value expression into the correct cases before solving.

(a) The inequality

\(|4x-1|\gt 9\)

means

\(4x-1\gt 9 \quad\text{or}\quad 4x-1\lt -9.\)

Solving these gives

\(4x\gt 10,\qquad x\gt \frac52,\)

or

\(4x\lt -8,\qquad x\lt -2.\)

Therefore

\(x\gt \frac52\quad\text{or}\quad x\lt -2.\)

(b) Let

\(u=\sqrt{x}.\)

Then \(x=u^2\), so the equation becomes

\(2u^2-11u+12=0.\)

Factorise:

\((2u-3)(u-4)=0.\)

So

\(u=\frac32 \quad\text{or}\quad u=4.\)

Since \(u=\sqrt{x}\),