Y+3 3/14=-1 4/21

To solve the equation \( y + 3 \frac{3}{14} = -1 \frac{4}{21} \), we can start by converting the mixed numbers into improper fractions. 1. Convert \( 3 \frac{3}{14} \): \[ 3 \frac{3}{14} = 3 + \frac{3}{14} = \frac{3 \times 14 + 3}{14} = \frac{42 + 3}{14} = \frac{45}{14} \] 2. Convert \( -1 \frac{4}{21} \): \[ -1 \frac{4}{21} = -1 - \frac{4}{21} = -\frac{21}{21} - \frac{4}{21} = -\frac{25}{21} \] Now we can rewrite the equation: \[ y + \frac{45}{14} = -\frac{25}{21} \] Next, isolate \( y \) by subtracting \( \frac{45}{14} \) from both sides: \[ y = -\frac{25}{21} - \frac{45}{14} \] To perform the subtraction, we need a common denominator. The least common multiple of 21 and 14 is 42. Now, convert both fractions to have a denominator of 42: - For \( -\frac{25}{21} \): \[ -\frac{25}{21} = -\frac{25 \times 2}{21 \times 2} = -\frac{50}{42} \] - For \( -\frac{45}{14} \): \[ -\frac{45}{14} = -\frac{45 \times 3}{14 \times 3} = -\frac{135}{42} \] Now substitute these into the equation: \[ y = -\frac{50}{42} - \frac{135}{42} \] Combine the fractions: \[ y = -\frac{50 + 135}{42} = -\frac{185}{42} \] This fraction can be simplified. The GCD of 185 and 42 is 1, so it cannot be simplified further. Thus, the solution is: \[ y = -\frac{185}{42} \] If desired, you can convert this to a mixed number: \[ y \approx -4 \frac{17}{42} \] So the final answer is: \[ y = -\frac{185}{42} \quad \text{or} \quad y \approx -4 \frac{17}{42} \]