Question

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

Answer 1

|d-5.000| <= 0.001

Answer 2

So,
d - 5 = 0.001
d * 1000 - 5 * 1000 = 0.001 * 1000
1000d - 5000 = 1
1000d - 5000 + 5000 = 1 + 5000
1000d = 5001
1000d / 1000 = 5001 / 1000
d = 5001/1000
or
d - 5 = -0.001
d * 1000 - 5 * 1000 = -0.001 * 1000
1000d - 5000 = -1
1000d - 5000 + 5000 = -1 + 5000
1000d = 4999
100d / 1000 = 4999 / 1000
d = 4999 / 1000

Would this be the correct solution?

Answer 3

not quite. You want d to be between those values:

4.999 <= d <= 5.001