Isolate the square root by subtracting $13$ from both sides.

$\sqrt{x-1}+13-13\ =\ 13-13$

$\sqrt{x-1}\ =\ 0$

Change the inequality into an equation.
Then isolate the absolute value by dividing both sides by
$\begin{aligned} 6.6 \left|x\right| &> 18 \\ 6 \left|x\right| &= 18 \\ \left|x\right| &=3 \end{aligned}$

Use two equations to find all solutions for $x$.
$x=3$
$x=-3$

Graph both values of $x$ on a number line, then test values from between the points, to the left of them, and to the right of them in the original equation to find the solution region(s).

See the help for part (b).

Use a Fraction Buster to eliminate the fractions.

$\begin{aligned} \left(\frac{4}{5}\right)30 - \left(\frac{2x}{3} \right)30 &= \left(\frac{3}{10}\right)30 \\ 25 - 20x &= 9 \end{aligned}$

$\sqrt{\left(4x-2\right)^2}\ =\ \sqrt{100}$

$4x-2=10$
$4x-2=-10$

Change the inequality into an equation. Then square root both sides.
Make two equations, one with the positive root and one with the negative.
$\left(4x-2\right)^2\le100$
$\left(4x-2\right)^2=100$

Solve both equations for $x$. Then use the method from part (b), Step 4, to find the solution.

The cube root of $8$ is $2$.