Question

For each of the figures, write Absolute Value in the form |x-c|=d, where c and d are some numbers, to satisfy the solution set.

Answer 1

a. An absolute value equation for figure a is |x - 4| = 4.

b. An absolute value equation for figure c is |x - 1| = 5.

Part a.

In order to write an absolute value equation for each figures, we would have to apply the following formula;

|x - middle point| = distance/2

Next, we would determine the midpoint between the given numbers 0 and 8;

Midpoint = (0 + 8)/2

Midpoint = 4.

For the distance, we have:

distance/2 = (8 - 0)/2

distance/2 = 4

Therefore, an absolute value equation for this figure can be written as follows;

|x - 4| = 4.

Part c.

We would determine the midpoint between the given numbers -4 and 6;

Midpoint = (-4 + 6)/2

Midpoint = 1.

For the distance, we have:

distance/2 = (6 - (-4))/2

distance/2 = 5

Therefore, an absolute value equation for this figure can be written as follows;

|x - 1| = 5.

Answer 2

`(a)`
`|0 - 8| = 8`

`(b)`
`|-4 - 6| = 10`

Explanation:

Given

Attached number lines

Required

Express as:
`|x - c| =d`

The two points on the number line represent x and c (in no particular) respectively.

Solving (a):

Let:

`x = 0`

`c = 8`

So:

`|x - c| =d`

`d =|0 - 8|`

Solve the expression in the absolute bracket

`d =|- 8|`

Remove absolute bracket

`d = 8`

So: the expression is;

`|0 - 8| = 8`

Solving (b):

Let:

`x = -4`

`c = 6`

So:

`|x - c| =d`

`d = |-4-6|`

Solve the expression in the absolute bracket

`d = |-10|`

Remove absolute bracket

`d = 10`

So: the expression is;

`|-4 - 6| = 10`