Write Absolute value equation that has the given solutions 4 and 11

| x + a | = | x + a |
As given in the question x=3 or x=9, replace first x by 3 and the other x by 9
| 3 + a | = | 9 + a |
3 + a = - ( 9 + a)
3 + a = -9 - a (Solving for a )
2a = -12
a = -12/2
a= -6
now, | x + a | = | 3 - 6 | = |-3| = 3
| x + a | = | 9 - 6 | = |3| = 3
Therefore, the answer is | x - 6 | = 3