(х-2) :5=2⅓:½

To solve the equation \((x - 2) : 5 = 2 \frac{1}{3} : \frac{1}{2}\), we'll start by converting the mixed number \(2 \frac{1}{3}\) into an improper fraction.

1. Convert \(2 \frac{1}{3}\) to an improper fraction: \[ 2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3} \]

2. Now we substitute this back into the equation: \[ (x - 2) : 5 = \frac{7}{3} : \frac{1}{2} \]

3. The ratio \(\frac{7}{3} : \frac{1}{2}\) can be rewritten as: \[ \frac{7}{3} \div \frac{1}{2} = \frac{7}{3} \times 2 = \frac{14}{3} \]

4. Now the equation becomes: \[ \frac{x - 2}{5} = \frac{14}{3} \]

5. To eliminate the fraction on the left, multiply both sides by 5: \[ x - 2 = \frac{14}{3} \times 5 \]

6. Calculate \(\frac{14}{3} \times 5\): \[ \frac{14 \times 5}{3} = \frac{70}{3} \]

7. Now the equation is: \[ x - 2 = \frac{70}{3} \]

8. Add 2 (which is \(\frac{6}{3}\)) to both sides: \[ x = \frac{70}{3} + \frac{6}{3} = \frac{70 + 6}{3} = \frac{76}{3} \]

So, the solution is: \[ x = \frac{76}{3} \]

In decimal form, this is approximately \(25.33\).