Final answer:
The absolute value equation that has the solutions x=-6 and x=10 is | x - 2 | = 16. Therefore, the correct equation is ∣x+6∣=∣x-10∣, option A.
Step-by-step explanation:
To write an absolute value equation that has the solutions x=-6 and x=10, we need an equation where these two values make the equation true. Absolute value equations involve the absolute value function, which returns the non-negative value of a number.
Since we have two solutions, the absolute value expression will be set equal to the distance between the two numbers. The distance between -6 and 10 on the number line is 16. Thus, the equation can be written as | x - 2 | = 16, where 2 is the midpoint between -6 and 10. This equation is satisfied by both x=-6 and x=10.
To write an absolute value equation with the solutions x = -6 and x = 10, we can use the formula for absolute value. The absolute value of a number is its distance from zero on the number line. When x = -6, the absolute value of x+6 is 0, and when x = 10, the absolute value of x-10 is 0.
Therefore, the correct equation is ∣x+6∣=∣x-10∣, option A.