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Official 2022 Paper 2 · Q14

Paper 2Algebra

Consider the two inequalities:

∣x+5∣<∣x+11∣|x+5|<|x+11|
∣x+11∣<∣x+1∣.|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.

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