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Question

A quality control inspector is in charge of inspecting drill bits that are produced on an assembly line. The diameter of a drill bit can be modeled by the equation |x − 0.525| = 0.01. Show your work in solving the equation to determine the minimum and maximum diameters of the drill bits.

Answer 1

There are 2 ways of solving absolute value equations. I like using the algebraic definition.

| x | = x, when x is positive or 0

         -x, when x is negative

 

Let's test this out.

| 4 | = .....since 4 is positive , the rule says do nothing to what is inside the absolute value sign....so your answer is 4.

| -6 | =....since -6 is negative, the rule says negate it, or equivalently, multiply by -1 to get your answer of 6. 

 

So in your problem, the expression x - .525 can represent either a positive or a negative number depending on what x value you pick.

If x - .525 represents a positive value or zero, according tothe definition above, you can just remove the absolute value sign to get the equation

x - .525 = .01 which leads to the answer x = .535.

 

If x - .525 represents a negative number, the rul says you can replace it with -1(x - .525) resulting i the equation

-1(x - .525) = .01

-x + .525 = .01

-x         = -.515

x          = .515

 

So x = .515 and x = .535 are your 2 answers. If you have the time, you should always check these

 

Check 1

| .515 - .525 | = | -.01 | = .01 Notice this answer came from when we considered x - .525 to be negative, and our value inside the 

                                                  absolute value sign WAS negative.

Check 2

| .535 - .525 | = | .01 | = .01

 

Hope this makes some sense.