8) $$ \frac{8}{10}=\frac{10}{x-6} $$

Question

UpStudy AI · Accepted Answer

To solve the equation:

$$
\frac{8}{10} = \frac{10}{x - 6}
$$

**Step 1: Cross-Multiply**

Cross-multiplying the fractions eliminates the denominators:

$$
8 \cdot (x - 6) = 10 \cdot 10
$$

$$
8(x - 6) = 100
$$

**Step 2: Distribute the 8**

Expand the left side of the equation:

$$
8x - 48 = 100
$$

**Step 3: Isolate the Variable Term**

Add 48 to both sides to move the constant term to the right:

$$
8x = 100 + 48
$$

$$
8x = 148
$$

**Step 4: Solve for $$ x $$**

Divide both sides by 8 to solve for $$ x $$:

$$
x = \frac{148}{8}
$$

Simplify the fraction by dividing both numerator and denominator by 4:

$$
x = \frac{37}{2} \quad \text{or} \quad x = 18.5
$$

**Final Answer:**
$$
x = 18.5
$$
$$ x = 18.5 $$

Solución de inteligencia artificial de Upstudy