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The solution set 3 and 7 are the true values of the absolute value equation
The absolute value equation that has a solution set of 3 and 7 is [tex]|x - 5| = 2[/tex]
The solution sets of the absolute value equation are given as:
x = {3, 7}
Calculate the mean of the solutions
[tex]x_1 = \frac{7 +3}{2}[/tex]
[tex]x_1 = 5[/tex]
Calculate the difference of the solutions divided by 2
[tex]x_2 = \frac{7 - 3}{2}[/tex]
[tex]x_2 = 2[/tex]
The absolute value equation is the represented as:
[tex]|x - x_1| - x_2 = 0[/tex]
Substitute known values
[tex]|x - 5| - 2 = 0[/tex]
Add 2 to both sides
[tex]|x - 5| = 2[/tex]
Hence, the absolute value equation that has the a solution set of 3 and 7 is [tex]|x - 5| = 2[/tex]
Read more about absolute value equation at:
https://brainly.com/question/2166748
Answer:
|x-5|=2
Step-by-step explanation:
Calculate the mean of the solutions
Calculate the difference of the solutions divided by 2
The absolute value equation is the represented as:
Substitute known values
Add 2 to both sides
Hence, the absolute value equation that has the a solution set of 3 and 7 is
Read more about absolute value equation at:
brainly.com/question/2166748