To determine which operator can be inserted to make the statement true, we will evaluate both sides of the inequality.
Let's simplify the left side:
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Calculate the left side: \[ 6 - 1/4 * 28 - 2 1/4 \]
Start by simplifying \(1/4 * 28\): \[ 1/4 * 28 = 7 \]
Now substitute back into the expression: \[ 6 - 7 - 2 1/4 \]
Convert \(2 1/4\) to an improper fraction: \[ 2 1/4 = \frac{9}{4} \]
Now we have: \[ 6 - 7 - \frac{9}{4} = -1 - \frac{9}{4} = -1 - 2.25 = -3.25 = -\frac{13}{4} \]
Thus, the left side simplifies to \(-\frac{13}{4}\).
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Calculate the right side: \[ 3/4 + 4 * 2 - 11 \]
Simplifying \(4 * 2\): \[ 4 * 2 = 8 \]
Now substitute back into the expression: \[ \frac{3}{4} + 8 - 11 \]
This simplifies to: \[ \frac{3}{4} + 8 - 11 = \frac{3}{4} + 8 - 11 = \frac{3}{4} - 3 = \frac{3}{4} - \frac{12}{4} = -\frac{9}{4} \]
So, the right side simplifies to \(-\frac{9}{4}\).
- Compare both sides:
- Left side: \(-\frac{13}{4}\)
- Right side: \(-\frac{9}{4}\)
Now we can evaluate which operator can be valid between these two sides:
- \(-\frac{13}{4} < -\frac{9}{4}\)
Thus, the correct operator to insert is: \[ < \] Therefore, the answer is \(<\).
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