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

To solve the equation \( \frac{1}{9}(2 m-16)=\frac{1}{3}(2 m+4) \), start by eliminating the fractions. Multiply both sides by 9 to get: \( 2m - 16 = 3(2m + 4) \). Now distribute on the right side: \( 2m - 16 = 6m + 12 \). Next, isolate \( m \) by moving all terms involving \( m \) to one side and constants to the other: \( 2m - 6m = 12 + 16 \) This simplifies to: \( -4m = 28 \). Finally, divide by -4: \( m = -7 \). Thus, the solution is \( m = -7 \). If you're wondering about how to catch any mistakes in such problems, always double-check your distribution and sign changes! Keeping a checklist while solving can help avoid those little slips that sometimes lead to big errors.