Question

If x = -4, which number best shows the value of |x|?
A. 4
B. -4
C. 0
D. 16

Answer 1

If (x = -4), the number that best represents the value of |x| is A. 4.

Step-by-step explanation:

The absolute value of a number is its distance from zero on the number line, irrespective of direction. Mathematically, \( |x| \) is defined as follows:

`\[ |x| = \begin{cases} x & \text{if } x \geq 0 \\ -x & \text{if } x < 0 \end{cases} \]`

In this case, (x = -4), which is less than zero. Therefore, |x| = -(-4) = 4. The absolute value of -4 is 4, and this aligns with option A.

It's crucial to understand that the absolute value is always non-negative, representing the magnitude of a real number. Option A (4) correctly reflects the absolute value of -4, as it captures the distance of -4 from zero on the number line, regardless of the negative sign.

In summary, when (x = -4), the value of |x| is 4, making option A the most accurate representation of the absolute value in this context.

Answer 2

The absolute value of -4 is 4.

Step-by-step explanation:

The absolute value of a number |x| represents the distance of x from zero on a number line. In this case, if x = -4, then |x| is equal to 4 because -4 is 4 units away from zero in the negative direction. Therefore, the best number to show the value of |x| is A. 4.