3. Solve each equation, and $$ \frac{1}{9}(2 m-16)=\frac{1}{3}(2 m+4) $$

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UpStudy AI · Accepted Answer

To solve the equation

$$
\frac{1}{9}(2m - 16) = \frac{1}{3}(2m + 4),
$$

follow these steps:

1. **Eliminate the Fractions:**
   
   To simplify the equation, multiply both sides by 9 (the least common multiple of 9 and 3) to eliminate the denominators:

$$
   9 \times \frac{1}{9}(2m - 16) = 9 \times \frac{1}{3}(2m + 4)
   $$

Simplifying both sides:

$$
   (2m - 16) = 3(2m + 4)
   $$

2. **Expand the Right Side:**
   
   Distribute the 3 on the right side of the equation:

$$
   2m - 16 = 6m + 12
   $$

3. **Collect Like Terms:**
   
   Bring all terms containing $$ m $$ to one side and constant terms to the other side. Subtract $$ 2m $$ from both sides:

$$
   -16 = 4m + 12
   $$

Next, subtract 12 from both sides:

$$
   -28 = 4m
   $$

4. **Solve for $$ m $$:**
   
   Divide both sides by 4 to isolate $$ m $$:

$$
   m = \frac{-28}{4} = -7
   $$

**Solution:** $$ m = -7 $$
$$ m = -7 $$

Solve each equation, and

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