Write the absolute value inequality in the form
x−bc that has the solution set x<−5 or x>7

|x - 1 |> 6,

Step-by-step explanation:

First we find the distance between the two points

-5 to 7

7 - -5 =7+5 = 12

We find 1/2 that distance

12/2 = 6

So we are looking for a greater-than inequality  because we are looking for the outsides because we want a less than and a greater than

|x - b |> c,

The center is 6 to that is c

|x - b |> 6,

To find the value of b

Let x = 7

7 -b =6

b=1

|x - 1 |> 6,

We can check by using -5

|-5 - 1 |> 6,

|x - 1| > 6

Step-by-step explanation:

x < -5 or x > 7

b is the centre:

(-5+7)/2 = 1

c is the distance from the centre

7 - 1 = 6

Or

1 - (-5) = 6

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

|x - 1| > 6

< 4, -5>

step-by-step explanation:

starting from g. we move 4 right and then 5 down to get to h. that means the vector is < 4, -5>