Add (1)/(2) to both sides of the equation.

$$3z = \frac{5}{4} + \frac{2}{4}$$ $$3z = \frac{7}{4}$$

$$z = \frac{7}{4} \times \frac{1}{3}$$ $$z = \frac{7}{12}$$

$$3\left(\frac{7}{12}\right) - \frac{1}{2} = \frac{7}{4} - \frac{1}{2} = \frac{7}{4} - \frac{2}{4} = \frac{5}{4}$$

The solution is correct.

$$\boxed{z = \frac{7}{12}}$$

$$x = 36 + 18$$ $$x = 54$$

$$54 - 18 = 36$$

The solution is correct.

$$\boxed{x = 54}$$

$$4x = 14 - 6$$ $$4x = 8$$

$$x = \frac{8}{4}$$ $$x = 2$$

$$4(2) + 6 = 8 + 6 = 14$$

The solution is correct.

$$\boxed{x = 2}$$

$$4 + 29 = 3v$$ $$33 = 3v$$

$$v = \frac{33}{3}$$ $$v = 11$$

$$3(11) - 29 = 33 - 29 = 4$$

The solution is correct.

$$\boxed{v = 11}$$

$$2x = 16 + 9$$ $$2x = 25$$

$$2\left(\frac{25}{2}\right) - 9 = 25 - 9 = 16$$

The solution is correct.

$$\boxed{x = \frac{25}{2}}$$

$$x = 10 \times 5$$ $$x = 50$$

$$\frac{50}{5} = 10$$

The solution is correct.

$$\boxed{x = 50}$$

$$1.6 = \frac{16}{10} = \frac{8}{5}$$

So the equation is:

$$\frac{2}{3}y = \frac{8}{5}$$

$$y = \frac{24}{10}$$ $$y = \frac{12}{5}$$ $$y = 2.4$$

$$\frac{2}{3}\left(\frac{12}{5}\right) = \frac{24}{15} = \frac{8}{5} = 1.6$$

The solution is correct.

$$\boxed{y = \frac{12}{5} \text{ or } 2.4}$$

$$-\frac{3}{4}x = \frac{5}{4} - \frac{1}{4}$$ $$-\frac{3}{4}x = \frac{4}{4}$$ $$-\frac{3}{4}x = 1$$

$$x = 1 \times \left(-\frac{4}{3}\right)$$ $$x = -\frac{4}{3}$$

$$\frac{1}{4} - \frac{3}{4}\left(-\frac{4}{3}\right) = \frac{1}{4} - (-1) = \frac{1}{4} + 1 = \frac{1}{4} + \frac{4}{4} = \frac{5}{4}$$

The solution is correct.

$$\boxed{x = -\frac{4}{3}}$$

$$x = \frac{4}{16}$$ $$x = \frac{1}{4}$$

$$\frac{1/4}{4} = \frac{1}{4} \times \frac{1}{4} = \frac{1}{16}$$

The solution is correct.

$$\boxed{x = \frac{1}{4}}$$

j) Solve $2a - 99 = 29$

$$2a = 29 + 99$$ $$2a = 128$$

$$a = \frac{128}{2}$$ $$a = 64$$

$$2(64) - 99 = 128 - 99 = 29$$

The solution is correct.

$$\boxed{a = 64}$$

k) Solve $\frac{5}{4}v - \frac{2}{3} = \frac{1}{3}$

$$\frac{5}{4}v = \frac{3}{3}$$ $$\frac{5}{4}v = 1$$

$$v = 1 \times \frac{4}{5}$$ $$v = \frac{4}{5}$$

$$\frac{5}{4}\left(\frac{4}{5}\right) - \frac{2}{3} = 1 - \frac{2}{3} = \frac{3}{3} - \frac{2}{3} = \frac{1}{3}$$

The solution is correct.

$$\boxed{v = \frac{4}{5}}$$

l) Solve $2x - \frac{1}{3} = \frac{7}{4}$

The common denominator for 4 and 3 is 12.

$$2x = \frac{7 \times 3}{4 \times 3} + \frac{1 \times 4}{3 \times 4}$$ $$2x = \frac{21}{12} + \frac{4}{12}$$ $$2x = \frac{25}{12}$$

$$x = \frac{25}{12} \times \frac{1}{2}$$ $$x = \frac{25}{24}$$

$$2\left(\frac{25}{24}\right) - \frac{1}{3} = \frac{25}{12} - \frac{1}{3} = \frac{25}{12} - \frac{4}{12} = \frac{21}{12} = \frac{7}{4}$$

The solution is correct.

$$\boxed{x = \frac{25}{24}}$$