Question

Special precision bolts are made by another machine. These are for jobs that require more exact measurements. The bolts must be within 0.01 mm of 8 mm. This is represented by |x – 8| < 0.01.

Write this inequality as a compound inequality without absolute value bars.






Solve the inequality.






Graph the solutions on a number line.






What do the solutions of the inequality mean for the bolt?

Answer 1

-.01 < x-8 < .01

7.99 < x< 8.01

see attached

The bolts must be greater than 7.99mm and less than 8.01 mm

Explanation:

|x – 8| < 0.01

to remove the absolute value bars, we need the positive and negative solutions

x-8 < .01 and x-8 > -.01

-.01 < x-8 < .01

solve

add 8 to each side

-.01 < x-8 < .01

8 + -.01 < x-8+8 < .01 +8

7.99 < x< 8.01