Final answer:
The absolute value equation for numbers x that are 8 units away from 4 is |x - 4| = 8, which has two solutions: x = 12 or x = -4.
Step-by-step explanation:
The absolute value equation representing all numbers x whose distance from 4 is 8 units can be written as |x - 4| = 8. The absolute value represents the distance from a number to another number on the number line, disregarding the direction. This equation simply states that the number x in question is 8 units away from 4, which could be either to the left or to the right of 4 on the number line. Therefore, x can have two possible solutions: x = 4 + 8 = 12 or x = 4 - 8 = -4.
The absolute value equation representing all numbers x whose distance from 4 is 8 units is |x - 4| = 8.
To find the absolute value equation, we use the definition that absolute value represents the distance from a number to zero on the number line. In this case, we want the distance from x to 4 to be 8 units. So, the equation becomes |x - 4| = 8.
This equation represents all the numbers whose distance from 4 is 8 units.