What term can you add to \( \frac{5}{6} x-4 \) to make it equivalent to \( \frac{1}{2} x-4 \) ?

To make the expression \( \frac{5}{6} x - 4 \) equivalent to \( \frac{1}{2} x - 4 \), we need to focus on the \( x \) terms only. First, let's express both fractions with a common denominator: The common denominator of 6 and 2 is 6. We can rewrite \( \frac{1}{2} \) as \( \frac{3}{6} \). Now, we want to find the difference between \( \frac{5}{6} x \) and \( \frac{3}{6} x \): \[ \frac{5}{6} x - \frac{3}{6} x = \frac{2}{6} x = \frac{1}{3} x \] So, if we add \( -\frac{1}{3} x \) to \( \frac{5}{6} x - 4 \), it will yield \( \frac{1}{2} x - 4 \). Therefore, the term to add is \( -\frac{1}{3}x \).