We want to find an absolute value equation such that its solutions are 4 and 11.
We will get: |x - 7.5| = 3.5
Let's see how we can get that.
We should start by the general absolute value equation:
|x - a| = b
This can be decomposed into two equations:
x - a = b
x - a = -b
Both of these must be true, one for each of the given solutions of the equation, now we need to replace these solutions. Let's use the largest solution in the equation where b is positive.
11 -a = b
4 - a = -b
Now we have a system of equations, to solve it we can see that we have the same variable isolated in the two equations, then we can rewrite:
11 - a = b
-(4 - a) = b
then:
11 - a = b = -(4 - a)
11 - a = -4 + a
11 + 4 = a + a
15 = 2*a
15/2 = a = 7.5
Then we can use:
11 - a = b
11 - 7.5 = b = 3.5
Now we know the values of a and b, we just need to replace them in the general equation to get:
|x - 7.5| = 3.5
This is the absolute value equation we were searching.
If you want to learn more, you can read:
https://brainly.com/question/11096127
