Question
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Tutor-Verified Answer
Answer
\( y = \frac{19}{2} \) or \( y = 9.5 \)
Solution
Untuk menyelesaikan persamaan:
\[
\frac{y - 2}{2} - \frac{y + 1}{3} = \frac{1}{4}
\]
Ikuti langkah-langkah berikut:
### Langkah 1: Mencari Penyebut Umum
Penyebut umum terkecil (KPK) dari 2, 3, dan 4 adalah 12. Kalikan kedua sisi persamaan dengan 12 untuk menghilangkan pecahan.
\[
12 \times \left( \frac{y - 2}{2} - \frac{y + 1}{3} \right) = 12 \times \frac{1}{4}
\]
### Langkah 2: Mengalikan dan Menyederhanakan
\[
12 \times \frac{y - 2}{2} - 12 \times \frac{y + 1}{3} = 12 \times \frac{1}{4}
\]
\[
6(y - 2) - 4(y + 1) = 3
\]
### Langkah 3: Mengembangkan
\[
6y - 12 - 4y - 4 = 3
\]
### Langkah 4: Menggabungkan Suku yang Sama
\[
(6y - 4y) + (-12 - 4) = 3
\]
\[
2y - 16 = 3
\]
### Langkah 5: Menyelesaikan untuk \( y \)
Tambahkan 16 ke kedua sisi:
\[
2y = 3 + 16
\]
\[
2y = 19
\]
Bagikan kedua sisi dengan 2:
\[
y = \frac{19}{2}
\]
\[
y = 9.5
\]
### Kesimpulan
Nilai dari \( y \) yang memenuhi persamaan tersebut adalah:
\[
y = \frac{19}{2} \quad \text{atau} \quad y = 9.5
\]
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Explain 
Simplify this solution Mind Expander
To solve the equation \( \frac{y-2}{2}-\frac{y+1}{3}=\frac{1}{4} \), we start by finding a common denominator. The least common multiple of 2, 3, and 4 is 12. We can rewrite each term with a denominator of 12: \[ \frac{6(y-2)}{12} - \frac{4(y+1)}{12} = \frac{3}{12} \] Now, multiply the entire equation by 12 to eliminate the denominators: \[ 6(y-2) - 4(y+1) = 3 \] Distributing gives us: \[ 6y - 12 - 4y - 4 = 3 \] Combining like terms: \[ 2y - 16 = 3 \] Add 16 to both sides: \[ 2y = 19 \] Now, divide by 2 to find \(y\): \[ y = \frac{19}{2} \quad \text{or} \quad y = 9.5 \] And there you have it! The solution to the equation is \(y = 9.5\).
