4. Solve for c: |c + 12| + 3 > 17 A. {c | c > or c < 2} B. {c | c > or c < 2} –2 –26 C. {c | c < or c > 2 } D. {c | c < or c > 2} –2 –26 5. Solve the absolute value inequality: |1 2w| < 5 – A. {c | 3 < c < B. {c | < c < 2} –2} –3 C. {c | 3 > c > D. {c | > c > 2} –2} –3 VII. Questions/Points to Ponder Solve the following problems involving absolute value. You need to cut a board to a length of 13 inches. If you can tolerate no more than a 2% relative error, what would be the boundaries of acceptable lengths when you measure the cut board? (Hint: Let x = actual length, and set up an inequality involving absolute value.) A manufacturer has a 0.6 oz tolerance for a bottle of salad dressing advertised as 16 oz. Write and solve an absolute value inequality that describes the acceptable volumes for (Hint: Let x = actual “16 oz” bottles. amount in a bottle, and set up an inequality involving absolute value.) Summary In this lesson you learned how to solve absolute value equations and absolute value inequalities. If a is a positive number, then the solution to the absolute value equation |x| = a is x = a or x = –a. There are two types of absolute value inequalities, each corresponding to a different procedure. If |x| < k, then x < k. If |x| > k, then x < or x > k. These –k< –k principles work for any positive number k.
4. Solve for c: |c + 12| + 3 > 17 A. {c | c > –2 or c < 2} B. {c | c > –26 or c < 2} C. {c | c < –2 or c > 2 } D. {c | c < –26 or c > 2} 5. Solve the absolute value inequality: |1 – 2w| < 5 A. {c | 3 < c < –2} B. {c | –3 < c < 2} C. {c | 3 > c > –2} D. {c | –3 > c > 2} VII. Questions/Points to Ponder Solve the following problems involving absolute value. You need to cut a board to a length of 13 inches. If you can tolerate no more than a 2% relative error, what would be the boundaries of acceptable lengths when you measure the cut board? (Hint: Let x = actual length, and set up an inequality involving absolute value.) A manufacturer has a 0.6 oz tolerance for a bottle of salad dressing advertised as 16 oz. Write and solve an absolute value inequality that describes the acceptable volumes for “16 oz” bottles. (Hint: Let x = actual amount in a bottle, and set up an inequality involving absolute value.) Summary In this lesson you learned how to solve absolute value equations and absolute value inequalities. If a is a positive number, then the solution to the absolute value equation |x| = a is x = a or x = –a. There are two types of absolute value inequalities, each corresponding to a different procedure. If |x| < k, then –k< x < k. If |x| > k, then x < –k or x > k. These principles work for any positive number k.
7-math-lm_mod3.docx