Question

Write the absolute value inequality in the form

|x−b| |x−b|>c that has the solution set x<−5 or x>7.
Answer:

Answer 1

|x - 1| > 6

Explanation:

b is the centre:

(-5 + 7)/2

2/2 = 1

b = 1

c is the distance from the centre

c = 7 - 1 = 6

Since it's an or case, > with the modulus

|x - 1| > 6

Answer 2

|x−1|>6

Explanation:

x<−5 or x>7.

The distance between -5 and 7 is

7 - -5 = 7+5 = 12

Divide that by 2

12/2 =6

That is the c value

We use the greater than since we have an or

|x−b|>6

Substitute a value in for x with an equals sign to determine b

x=7

7-b =6

b=1

|x−1|>6