Questions: Which sign makes the statement true? -6 1/4 ? -∛79

Solution Steps

To determine which sign makes the statement true, we need to compare the two numbers: \(-6 \frac{1}{4}\) and \(-\sqrt[3]{79}\). We will calculate the decimal values of both numbers and then compare them to decide which inequality sign (>, <, or =) makes the statement true.

The mixed number \(-6 \frac{1}{4}\) can be converted to a decimal as follows: \[ -6 \frac{1}{4} = -6 - \frac{1}{4} = -6.25 \]

Next, we calculate the cube root of \(79\) and negate it: \[ -\sqrt[3]{79} \approx -4.2908 \]

Now we compare the two decimal values: \[ -6.25 \quad \text{and} \quad -4.2908 \] Since \(-6.25 < -4.2908\), we can conclude that: \[ -6 \frac{1}{4} < -\sqrt[3]{79} \]

Final Answer