We need to solve for $x$ in each of the given equations.

1. Problem Description

We need to solve for $x$ in each of the given equations.

2. Solution Steps

1. $\frac{7}{x} = 21$

Multiply both sides by $x$:

$7 = 21x$

Divide both sides by 21:

$x = \frac{7}{21} = \frac{1}{3}$

2. $30 = \frac{6}{x}$

Multiply both sides by $x$:

$30x = 6$

Divide both sides by 30:

$x = \frac{6}{30} = \frac{1}{5}$

3. $\frac{5}{x} = 3$

Multiply both sides by $x$:

$5 = 3x$

Divide both sides by 3:

$x = \frac{5}{3}$

4. $\frac{9}{x} = -3$

Multiply both sides by $x$:

$9 = -3x$

Divide both sides by -3:

$x = \frac{9}{-3} = -3$

5. $11 = \frac{5}{x}$

Multiply both sides by $x$:

$11x = 5$

Divide both sides by 11:

$x = \frac{5}{11}$

6. $-2 = \frac{4}{x}$

Multiply both sides by $x$:

$-2x = 4$

Divide both sides by -2:

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

7. $\frac{x}{4} = \frac{3}{2}$

Multiply both sides by 4:

$x = \frac{3}{2} \times 4 = 3 \times 2 = 6$

8. $\frac{x}{3} = 1\frac{1}{4} = \frac{5}{4}$

Multiply both sides by 3:

$x = \frac{5}{4} \times 3 = \frac{15}{4}$

9. $\frac{x+1}{3} = \frac{x-1}{4}$

Cross-multiply:

$4(x+1) = 3(x-1)$

$4x + 4 = 3x - 3$

$4x - 3x = -3 - 4$

$x = -7$

3. Final Answer

1. $x = \frac{1}{3}$

2. $x = \frac{1}{5}$

3. $x = \frac{5}{3}$

4. $x = -3$

5. $x = \frac{5}{11}$

6. $x = -2$

7. $x = 6$

8. $x = \frac{15}{4}$

9. $x = -7$