Question

Write an absolute value equation that has the solutions x=2 and x=9

Answer 1

Hi, i think it is like
Ia+xI=-x-a
  a+2=-a-x
   a+2=-a-9
     2a=-11
        a=-5.5
so Ix-5.5I=3.5
i think it is correct you can test 

Answer 2

The answer is |2x - 11| = 7 The absolute value betwwen two numbers is the distance the two numbers are apart in the numbers line. Let's remember that the distance betwwen to numbers is the algebraic sum of the two numbers divided by two. In this case, the distance between 2 and 9 is d: (2+9)/2 = 11/2 Now, we know that |x+d| = |x+d|, with x= 2 and x=9, so: 2 + d = -9 -d 2d = -11 d = -11/2 Now, replacing one of the absolute values, in this case we will replace with x=2, but if we replace with x=9 the result should be the same: |x - 11/2| = -7/2, or, multiplying both sides by two: |2x - 11| = -7