Find the value of x such that:
(i) `-2/3=14/x`, (ii) `8/-3 = x/6`, (iii) `5/9 = x/(-27)`
(iv) `11/6 = -55/x`, (v) `15/x =-3`, (vi) `-36/x =2`

Answer

Let's solve the equations step by step:

### (i) Solve for x in the equation:
\[ -\frac{2}{3} = \frac{14}{x} \]

**Step 1:** Cross-multiply to eliminate the fractions:
\[ -2 \cdot x = 3 \cdot 14 \]

**Step 2:** Simplify the right side:
\[ -2x = 42 \]

**Step 3:** Divide both sides by -2 to solve for x:
\[ x = \frac{42}{-2} = -21 \]

### (ii) Solve for x in the equation:
\[ \frac{8}{-3} = \frac{x}{6} \]

**Step 1:** Cross-multiply:
\[ 8 \cdot 6 = -3 \cdot x \]

**Step 2:** Simplify the left side:
\[ 48 = -3x \]

**Step 3:** Divide both sides by -3:
\[ x = \frac{48}{-3} = -16 \]

### (iii) Solve for x in the equation:
\[ \frac{5}{9} = \frac{x}{-27} \]

**Step 1:** Cross-multiply:
\[ 5 \cdot (-27) = 9 \cdot x \]

**Step 2:** Simplify the left side:
\[ -135 = 9x \]

**Step 3:** Divide both sides by 9:
\[ x = \frac{-135}{9} = -15 \]

### (iv) Solve for x in the equation:
\[ \frac{11}{6} = \frac{-55}{x} \]

**Step 1:** Cross-multiply:
\[ 11x = -55 \cdot 6 \]

**Step 2:** Simplify the right side:
\[ 11x = -330 \]

**Step 3:** Divide both sides by 11:
\[ x = \frac{-330}{11} = -30 \]

### (v) Solve for x in the equation:
\[ \frac{15}{x} = -3 \]

**Step 1:** Cross-multiply:
\[ 15 = -3x \]

**Step 2:** Divide both sides by -3:
\[ x = \frac{15}{-3} = -5 \]

### (vi) Solve for x in the equation:
\[ \frac{-36}{x} = 2 \]

**Step 1:** Cross-multiply:
\[ -36 = 2x \]

**Step 2:** Divide both sides by 2:
\[ x = \frac{-36}{2} = -18 \]

### Summary of Solutions:
1. \( x = -21 \)
2. \( x = -16 \)
3. \( x = -15 \)
4. \( x = -30 \)
5. \( x = -5 \)
6. \( x = -18 \)