Write an absolute value equation that has the solutions x = -6 and x = 10

Answer 1

An absolute value equation that has the solutions x = -6 and x = 10 can be written as:

|x - a| = 16

where a is a constant value.

To find the value of a, let's substitute the first solution, x = -6 into the equation:

|-6 - a| = 16

Since |-6 - a| = |6 + a|, we can rewrite the equation as:

|6 + a| = 16

Since x = -6 is a solution, this equation states that the distance between 6 and a is 16, which means that a must be 10 to satisfy this equation.

Therefore, the absolute value equation that has the solutions x = -6 and x = 10 is:

|x - 10| = 16