Solve the equation $$ \frac{1}{7}(6 t-4)=\frac{1}{14}(t+4) $$

Question

UpStudy AI · Accepted Answer

To solve the equation:

$$
\frac{1}{7}(6t - 4) = \frac{1}{14}(t + 4)
$$

follow these steps:

### Step 1: Eliminate the Fractions

To simplify the equation, multiply both sides by the least common multiple (LCM) of the denominators 7 and 14. The LCM of 7 and 14 is **14**.

$$
14 \times \frac{1}{7}(6t - 4) = 14 \times \frac{1}{14}(t + 4)
$$

### Step 2: Simplify Both Sides

$$
2 \times (6t - 4) = 1 \times (t + 4)
$$

$$
2(6t - 4) = t + 4
$$

$$
12t - 8 = t + 4
$$

### Step 3: Solve for $$ t $$

1. **Subtract $$ t $$ from both sides:**

$$
   12t - t - 8 = t - t + 4
   $$

$$
   11t - 8 = 4
   $$

2. **Add 8 to both sides:**

$$
   11t - 8 + 8 = 4 + 8
   $$

$$
   11t = 12
   $$

3. **Divide both sides by 11:**

$$
   t = \frac{12}{11}
   $$

### Step 4: Simplify the Fraction (Optional)

$$
t = 1 \frac{1}{11} \quad \text{or approximately} \quad t \approx 1.0909
$$

### **Final Answer**

$$
t = \frac{12}{11}
$$
$$ t = \frac{12}{11} $$

Solve the equation \[ \frac{1}{7}(6 t-4)=\frac{1}{14}(t+4) \]