Question

2. Another machine is used to make 10 mm long bolts. For this machine, the bolts must have an error of less than 0.1 mm to be accepted. This can be represented by |x – 10| < 0.1.
a. Write this inequality as a compound inequality without absolute value bars. b. Solve the compound inequality.
c. Graph the solutions on a number line.
d. What do the solutions of the inequality mean for the bolt?

Answer 1

Part AAnswer: -0.1 < x-10 < 0.1
Use the rule |x| < k leads to -k < x < k for some positive number k

Part BAnswer: 9.9 < x < 10.1
Add 10 to all three sides of -0.1 < x-10 < 0.1


Part C
Draw out a number line. Plot open circles at 9.9 and 10.1 on the number line. Shade the region between the open circles. The open circles indicates "do not include this point as part of the solution set"

Part D
The solution 9.9 < x < 10.1 means that anything between 9.9 and 10.1 is accepted as a bolt length (even if the exact measurement isn't 10 mm on the dot). The length 9.9 is not allowed; neither is 10.1


Hope this helped! (: