Question

Write an absolute value equation that has the solutions x=-6 and x=10. a) |x + 6| = 10 b) |x - 6| = 10 c) |x + 10| = 6 d) |x - 10| = 6

Answer 1

The correct absolute value equation that has the solutions x=-6 and x=10 is: |x - 6| = 10. The correct option is b) |x - 6| = 10.

Step-by-step explanation:

To find an absolute value equation that has solutions x=-6 and x=10, we need an equation where both -6 and 10 satisfy the equation when substituted in place of x. Considering the nature of absolute values, the equation must equate to the positive distance of both numbers from some point on the number line.

Recall that the absolute value of a number is its distance from zero on the number line regardless of direction.

Therefore, the distance of both -6 and 10 from the point that is equidistant from them is 16 (distance between -6 and 10 on the number line). Hence, we look for an equation with an absolute value equaling half of 16, which is 8.

The correct absolute value equation that has the solutions x=-6 and x=10 is: b) |x - 6| = 10.

To explain how we arrived at this answer:

We know that the absolute value of a number is its distance from zero on the number line.Since we have the solutions x=-6 and x=10, we want to find the equation such that the absolute value of x minus a number equals 10.Hence, the equation |x - 6| = 10 represents the correct absolute value equation.