tmua 2022 Q14

tmua · Uk · paper2 1 marks Inequalities Absolute Value Inequality
Consider the two inequalities:
$$\begin{aligned} & | x + 5 | < | x + 11 | \\ & | x + 11 | < | x + 1 | \end{aligned}$$
Which one of the following is correct?
A There is no real number for which both inequalities are true.
B There is exactly one real number for which both inequalities are true.
C The real numbers for which both inequalities are true form an interval of length 1 .
D The real numbers for which both inequalities are true form an interval of length 2 .
E The real numbers for which both inequalities are true form an interval of length 3 .
F The real numbers for which both inequalities are true form an interval of length 4 .
G The real numbers for which both inequalities are true form an interval of length 5 .
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Consider the two inequalities:

$$\begin{aligned}
& | x + 5 | < | x + 11 | \\
& | x + 11 | < | x + 1 |
\end{aligned}$$

Which one of the following is correct?\\
A There is no real number for which both inequalities are true.

B There is exactly one real number for which both inequalities are true.

C The real numbers for which both inequalities are true form an interval of length 1 .

D The real numbers for which both inequalities are true form an interval of length 2 .

E The real numbers for which both inequalities are true form an interval of length 3 .

F The real numbers for which both inequalities are true form an interval of length 4 .

G The real numbers for which both inequalities are true form an interval of length 5 .