Amachine makes bolts that are 12 mm long. the bolts are considered acceptable if they are within 0.2 mm of 12 mm. what is the longest the bolt can be and still be acceptable? the biggest the bolt can be is 6 what is the shortest the bolt can be and still be acceptable?

The correct answers are:

The longest bolt can be 12.2 mm and the shortest can be 11.8 mm.

Explanation:

Since this is a problem about the distance from a number, we will use an absolute value equation.  We use these for these types of problems because the bolts can be either shorter or longer than the target; we must consider both answers.  The operation that makes a number positive without changing its value is absolute value, so our equation is

|x - 12| = 0.2

We split this into two equations:

x - 12 = 0.2 or x - 12 = -0.2

Add 12 to both sides of both equations:

x - 12 + 12 = 0.2+12 or x - 12 + 12 = -0.2 + 12

x = 12.2 or x = 11.8