$$ 4=-\frac{5 y}{4}+\frac{y+5}{6} $$ INSTRUCTION: Give your answer as a simplified fraction. Answer: $$ y=\square $$

Question

UpStudy AI · Accepted Answer

1. Multiply both sides by the least common denominator (LCD) of 4 and 6, which is 12:

$$
12 \cdot 4 = 12 \left(-\frac{5y}{4}\right) + 12 \left(\frac{y+5}{6}\right)
$$

2. Simplify each term:

$$
48 = -15y + 2(y+5)
$$

3. Distribute in the second term:

$$
48 = -15y + 2y + 10
$$

4. Combine like terms:

$$
48 = -13y + 10
$$

5. Isolate the $$ y $$-term by subtracting 10 from both sides:

$$
48 - 10 = -13y \quad \Rightarrow \quad 38 = -13y
$$

6. Solve for $$ y $$ by dividing both sides by $$-13$$:

$$
y = -\frac{38}{13}
$$

$$ y=-\frac{38}{13} $$
$$ y = -\frac{38}{13} $$

INSTRUCTION: Give your answer as a simplified fraction.
Answer: