SOLUTION: In the manufacture of​ widgets, the average dimension of a part is 0.005 cm. Using the​ absolute-value symbol, express the fact that an individual measurement x of a part does

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Question 1186160: In the manufacture of​ widgets, the average dimension of a part is 0.005 cm. Using the​ absolute-value symbol, express the fact that an individual measurement x of a part does not differ from the average by more than 0.0006 cm.
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.
In the manufacture of​ widgets, the average dimension of a part is 0.005 cm.
Using the​ absolute-value symbol, express the fact that an individual measurement x of a part
does not differ from the average by more than 0.0006 cm.
~~~~~~~~~~~~~~~ 

This inequality is


    | x - 0.005 | <= 0.0006  centimeters.    ANSWER

Solved.


------------


What you need to learn and memorize,  is  THIS:


        - the average and the concrete measurement difference are under the absolute value sign;

        - the "tolerance" value is out the absolute sign in the other part of the inequality.



Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
i believe the equation is going to be:

abs(x - .005) <= .0006

the absolute value property of an equation is such that:

if the expression inside the absolute value sign is positive, then the inequality becomes:

(x - .005) <= .0006

if the expression inside the absolute value sign is negative, then the inequality becomes:

-(x - .005) <= .0006

we'll solve for when the expression inside the absolute value sign is positive.

(x - .005) <= .0006

remove the parentheses to get:

x - .005 <= .0006

add .005 to both sides of the inequality to get:

x <= .0006 + .005

solve for x to get:

x <= .0056

now we'll solve for when the expression within the absolute value sign is negative.

-(x - .005) <= .0006

multiply both sides of this inequality by -1 to get:

(x - .005) >= -.0006

multiplying both sides of an inequality by a negative number reverses the inequality.

that's why the inequality is now >= rather than <=.

remove the parentheses to get:

x - .005 >= -.0006

add .005 to both sides of the inequality to get:

x >= -.0006 + .005

solve for x to get:

x >= .0044

your solution is that the absolute value inequality is:

|x - .005| <= .0006

this leads to the value of x being greater than .0044 and less than .0056, which can be expressed as:

.0044 <= x <= .0056




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