To determine the additional operation that should be included in the expression \( \frac{5}{4}x + 6 + _\) so that it becomes equivalent to \( \frac{1}{2}x + 6 \), we can follow these steps:
-
Write the two expressions we want to be equal: \[ \frac{5}{4}x + 6 + _ = \frac{1}{2}x + 6 \]
-
Isolate the variable parts (remove the constant 6 from both sides): \[ \frac{5}{4}x + _ = \frac{1}{2}x \]
-
Convert \( \frac{1}{2}x \) into a fraction with a denominator of 4 for easier comparison: \[ \frac{1}{2} = \frac{2}{4} \] So, \( \frac{1}{2}x = \frac{2}{4}x \).
-
Rewrite the equation: \[ \frac{5}{4}x + _ = \frac{2}{4}x \]
-
Now isolate \( _ \): \[ _ = \frac{2}{4}x - \frac{5}{4}x \]
-
Perform the subtraction: \[ _ = \left( \frac{2}{4} - \frac{5}{4} \right)x = \frac{-3}{4}x \]
Thus, to make the original expression equivalent to \( \frac{1}{2}x + 6 \), the additional operation should be \( -\frac{3}{4}x \).
The correct answer is:
- \(-\frac{3}{4}x\)
1 answer