Choose the statement that correctly compares the two numbers

Question

-2 PI and -8

A. Since PI < 4, then 2 PI < 2(4) so -2 PI > -8

B. Since PI < 4, then 2 PI < 2 •4 so -2 PI < -8

C. Since PI > 4, then 2 PI > 2•4 so -2 PI > -8

D. Since PI > 4, then 2 PI > 2•4 so -2 PI < -8

Answer 1

To compare the numbers \(-2\pi\) and \(-8\), we can simplify the problem using the known approximate value of \(\pi\), which is about 3.14.

Calculating \(2\pi\): \[ 2\pi \approx 2 \times 3.14 = 6.28 \] Thus, \[ -2\pi \approx -6.28 \]

Now, to compare \(-6.28\) with \(-8\): Since \(-6.28\) is greater than \(-8\) (because on the number line, -6.28 is to the right of -8), we know that:

\[ -2\pi > -8 \]

Now, let's examine the statements:

A. Since \(\pi < 4\), then \(2\pi < 2(4)\), so \(-2\pi > -8\) — This is TRUE.

B. Since \(\pi < 4\), then \(2\pi < 2 \cdot 4\) so \(-2\pi < -8\) — This is FALSE.

C. Since \(\pi > 4\), then \(2\pi > 2 \cdot 4\) so \(-2\pi > -8\) — This is FALSE (because \(\pi\) is not greater than 4).

D. Since \(\pi > 4\), then \(2\pi > 2 \cdot 4\) so \(-2\pi < -8\) — This is FALSE (for the same reason).

The correct choice is option A.