we conclude that the absolute value equation with the solutions x = 1.5 and x = 8.5 is:
|x - 5| = 3.5
How to write an absolute value equation that has the solutions x=1.5 and x=8.5?
A general absolute value equation is written as:
|x - a| = b
This can be rewritten into two simpler equations, which are:
x - a = b
x - a = -b
Now we can replace the given solutions, let's use the larger solution in the first equation and the smaller solution on the second one:
8.5 - a = b
1.5 - a = -b
Now we have a system of linear equations to solve, if we substitute the first equation into the second one, we will get:
1.5 - a = -(8.5 - a)
Now we can solve this for a:
1.5 - a = -8.5 + a
1.5 + 8.5 = 2a
10/2 = a = 5
To find the value of b we can use any of the two equations of the system:
8.5 - a = b
8.5 - 5 = b
3.5 = b
In this way, we conclude that the absolute value equation with the solutions x = 1.5 and x = 8.5 is:
|x - 5| = 3.5
If you want to learn more about absolute value equations:
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