Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
x = 17
\]
Solution
Quyidagi tenglamani yechamiz:
\[
\frac{5x - 7}{12} - \frac{x - 5}{8} = 5
\]
**1. Tenglamadagi kesrlarni yo'q qilish uchun eng kichik umumiy ko‘paytuvchidan (EKUK) foydalanamiz. 12 va 8 uchun EKUK = 24.**
Tenglamaning har ikki tomonini 24 ga ko‘paytiramiz:
\[
24 \cdot \left( \frac{5x - 7}{12} - \frac{x - 5}{8} \right) = 24 \cdot 5
\]
**2. Kesrlarni yo'qotamiz va tarqatamiz:**
\[
2(5x - 7) - 3(x - 5) = 120
\]
**3. Qavslarni ochamiz va ko‘paytmalarni bajarimiz:**
\[
10x - 14 - 3x + 15 = 120
\]
**4. O‘xshash xonalarni birlashtiramiz:**
\[
7x + 1 = 120
\]
**5. 1 ni ayiramiz:**
\[
7x = 119
\]
**6. X ni topish uchun 7 ga bo‘lamiz:**
\[
x = \frac{119}{7} = 17
\]
**Natija:**
\[
x = 17
\]
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Simplify this solution Beyond the Answer
To solve the equation \( \frac{5x-7}{12}-\frac{x-5}{8}=5 \), start by eliminating the fractions. Find a common denominator, which is 24. Multiply each term by 24: \[ 24 \left( \frac{5x-7}{12} \right) - 24 \left( \frac{x-5}{8} \right) = 24 \cdot 5 \] This simplifies to: \[ 2(5x - 7) - 3(x - 5) = 120 \] Expanding both sides gives: \[ 10x - 14 - 3x + 15 = 120 \] Combine like terms: \[ 7x + 1 = 120 \] Now, subtract 1 from both sides: \[ 7x = 119 \] Finally, divide by 7: \[ x = 17 \] So the solution to the equation is \( x = 17 \).
