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.

| d - 5.000| = 0.001

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

and

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

| d - 5.000| = 0.001

Wrongg

wrong

d = 5.001 mm and d = 4.999 mm are the boundary values for the acceptable diameters of the valve.

To find the boundary values for the acceptable diameters of the valve, we can write and solve an absolute value equation.

The equation representing the diameter of the valve is | d - 5.000 | = 0.001, where d represents the diameter we are trying to find.

To solve the equation, we need to isolate the absolute value expression and solve for d.

First, we can remove the absolute value signs by breaking the equation into two cases:

Case 1: (d - 5.000) = 0.001

By adding 5 to both sides of the equation, we get:

d = 5.001

Case 2: -(d - 5.000) = 0.001

By distributing the negative sign inside the absolute value, we get:

-d + 5.000 = 0.001

Subtracting 5 from both sides of the equation, we have:

-d = -4.999

Multiplying both sides by -1 (to isolate d), we get:

d = 4.999

Therefore, the boundary values for the acceptable diameters of the valve are 4.999 mm and 5.001 mm.