Manufactured bolts can’t be too long or too short or they might not fit where they need to. determine which bolts will work and which won’t. show your work for all steps. 1. a machine makes bolts that are 12 mm long. the bolts are considered acceptable if they are within 0.2 mm of 12 mm. a. what is the longest the bolt can be and still be acceptable? b. what is the shortest the bolt can be and still be acceptable? 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? 3. 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. a. write this inequality as a compound inequality without absolute value bars. b. solve the inequality. c. graph the solutions on a number line. d. what do the solutions of the inequality mean for the bolt? 4. suppose 1.5-inch long bolts are made by another machine and have to be within 0.125 inches of 1.5 inches. a. write an absolute value inequality to represent this tolerance. b. rewrite the absolute value inequality as a compound inequality without absolute value bars. c. solve the compound inequality. d. what does the solution mean for the bolts? e. give an example of one acceptable length for a bolt. f. give an example of one non-acceptable length for a bolt.