Find the value of x, if `4:5 = x:10 `.

Answer

To solve the equation \(4:5 = x:10\), we can follow these steps:

### Step 1: Write the ratio as a fraction
We start by converting the ratios into fractions:
\[ \frac{4}{5} = \frac{x}{10} \]

### Step 2: Cross-multiply
Next, we cross-multiply to eliminate the fractions. This means we multiply the numerator of one fraction by the denominator of the other fraction:
\[ 4 \cdot 10 = 5 \cdot x \]
This simplifies to:
\[ 40 = 5x \]

### Step 3: Solve for \(x\)
Now, we need to isolate \(x\). To do this, we divide both sides of the equation by 5:
\[ x = \frac{40}{5} \]
Calculating the right side gives:
\[ x = 8 \]

### Final Answer
Thus, the value of \(x\) is:
\[ \boxed{8} \]

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