The diameter of a value for the space shuttle must be within 0.001mm of 5mm. write and solve an absolute value equation to find the boundary values for the acceptable diameters of the valve.

Since it is within 0.001mm, then that means that if the diameter is 5+x, 
5+x>4.999 (due to that 5-0.001=4.999) and 5+x<5.001 (since 5+0.001=5.001 and therefore has to be less than that), getting 4.999<5+x<5.001. Subtracting 5, we get -0.001<x<0.001. If we get the absolute value of everything, that means that |-0.001|>|x|<|0.001| (Note that since getting the absolute value of a negative number requires you to multiply it by -1, we switch the inequality around).Adding 5 back to it, we get 5+|x|>5+|0.001|