Find x such that:
(i) `frac(-1)(5)=frac(8)(x)`
(ii) `frac(7)(-3)=frac(x)(6)`
(iii) `frac(3)(5)=frac(x)(-25)`
(iv) `frac(13)(6)=frac(-65)(x)`
(v) `frac(16)(x)=-4`
(vi) `frac(-48)(x)=2`

Answer

Let's solve each part step by step:

### Part (i):
\[ \frac{-1}{5} = \frac{8}{x} \]

**Step 1:** Cross multiply the fractions.
\[ -1 \cdot x = 5 \cdot 8 \]

**Step 2:** Simplify the right side.
\[ -x = 40 \]

**Step 3:** Multiply both sides by -1 to solve for \(x\).
\[ x = -40 \]

### Part (ii):
\[ \frac{7}{-3} = \frac{x}{6} \]

**Step 1:** Cross multiply the fractions.
\[ 7 \cdot 6 = -3 \cdot x \]

**Step 2:** Simplify the left side.
\[ 42 = -3x \]

**Step 3:** Divide both sides by -3 to solve for \(x\).
\[ x = \frac{42}{-3} = -14 \]

### Part (iii):
\[ \frac{3}{5} = \frac{x}{-25} \]

**Step 1:** Cross multiply the fractions.
\[ 3 \cdot (-25) = 5 \cdot x \]

**Step 2:** Simplify the left side.
\[ -75 = 5x \]

**Step 3:** Divide both sides by 5 to solve for \(x\).
\[ x = \frac{-75}{5} = -15 \]

### Part (iv):
\[ \frac{13}{6} = \frac{-65}{x} \]

**Step 1:** Cross multiply the fractions.
\[ 13 \cdot x = 6 \cdot (-65) \]

**Step 2:** Simplify the right side.
\[ 13x = -390 \]

**Step 3:** Divide both sides by 13 to solve for \(x\).
\[ x = \frac{-390}{13} = -30 \]

### Part (v):
\[ \frac{16}{x} = -4 \]

**Step 1:** Rewrite -4 as a fraction.
\[ \frac{16}{x} = \frac{-4}{1} \]

**Step 2:** Cross multiply the fractions.
\[ 16 \cdot 1 = -4 \cdot x \]

**Step 3:** Simplify the left side.
\[ 16 = -4x \]

**Step 4:** Divide both sides by -4 to solve for \(x\).
\[ x = \frac{16}{-4} = -4 \]

### Part (vi):
\[ \frac{-48}{x} = 2 \]

**Step 1:** Rewrite 2 as a fraction.
\[ \frac{-48}{x} = \frac{2}{1} \]

**Step 2:** Cross multiply the fractions.
\[ -48 \cdot 1 = 2 \cdot x \]

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

**Step 4:** Divide both sides by 2 to solve for \(x\).
\[ x = \frac{-48}{2} = -24 \]

### Summary of Solutions:
- (i) \(x = -40\)
- (ii) \(x = -14\)
- (iii) \(x = -15\)
- (iv) \(x = -30\)
- (v) \(x = -4\)
- (vi) \(x = -24\)