Consider the two inequalities: |x + 5| < |x + 11| |x + 11| < |x + 1| Which one of the following is correct?
- AThere is no real number for which both inequalities are true.
- BThere is exactly one real number for which both inequalities are true.
- CThe real numbers for which both inequalities are true form an interval of length 1.
- DThe real numbers for which both inequalities are true form an interval of length 2.
- EThe real numbers for which both inequalities are true form an interval of length 3.
- FThe real numbers for which both inequalities are true form an interval of length 4.
- GThe real numbers for which both inequalities are true form an interval of length 5.
Show the answer and worked solution
answer · D
- AThere is no real number for which both inequalities are true.
- BThere is exactly one real number for which both inequalities are true.
- CThe real numbers for which both inequalities are true form an interval of length 1.
- DThe real numbers for which both inequalities are true form an interval of length 2.
- EThe real numbers for which both inequalities are true form an interval of length 3.
- FThe real numbers for which both inequalities are true form an interval of length 4.
- GThe real numbers for which both inequalities are true form an interval of length 5.
Read each as a comparison of distances. The first says x is closer to −5 than to −11, which puts it beyond their midpoint: x > −8. The second says x is closer to −11 than to −1, so x < −6. Together they give −8 < x < −6, an interval of length 2.