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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.

For each of the figures, write Absolute Value in the form |x-c|=d, where c and d are-example-1
For each of the figures, write Absolute Value in the form |x-c|=d, where c and d are-example-1
For each of the figures, write Absolute Value in the form |x-c|=d, where c and d are-example-2

2 Answers

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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.

For each of the figures, write Absolute Value in the form |x-c|=d, where c and d are-example-1
For each of the figures, write Absolute Value in the form |x-c|=d, where c and d are-example-2
User Macosso
by
7.8k points
2 votes

Answer:


(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

User Ratnesh Maurya
by
7.6k points

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