Find a true inequality that involves the real number $\frac { 10 } { 7 }$ .

A) $\frac { 10 } { 7 } > \frac { 3 } { 7 }$
B) $\frac { 10 } { 7 } < - \frac { 17 } { 7 }$
C) $\frac { 10 } { 7 } < - \frac { 4 } { 3 }$
D) $107>−76\frac { 10 } { 7 } > - \frac { 7 } { 6 }$
E) $\frac { 10 } { 7 } > - \frac { 3 } { 7 }$

Question

Find a true inequality that involves the real number − 10 7 - \frac { 10 } { 7 } − 7 10 .A) \frac { 3 } { 7 }> − 10 7 > 3 7 - \frac { 10 } { 7 } > \frac { 3 } { 7 } − 7 10 > 7 3 B) − 10 7 < − 17 7 - \frac { 10 } { 7 } < - \frac { 17 } { 7 } − 7 10 < − 7 17 C) − 10 7 < − 4 3 - \frac { 10 } { 7 } < - \frac { 4 } { 3 } − 7 10 < − 3 4 D) - \frac { 7 } { 6 }> 10 7 > − 7 6 \frac { 10 } { 7 } > - \frac { 7 } { 6 } 7 10 > − 6 7 E) - \frac { 3 } { 7 }> − 10 7 > − 3 7 - \frac { 10 } { 7 } > - \frac { 3 } { 7 } − 7 10 > − 7 3

Emily Karpel · Accepted Answer

Final Answer : C, Explanation :   We can see that   − 10 7 - \frac { 10 } { 7 } − 7 10 ​   is negative and less than 1. Option C is the only true inequality that satisfies these conditions since   − 4 3 - \frac { 4 } { 3 } − 3 4 ​   is greater in magnitude than   − 10 7 - \frac { 10 } { 7 } − 7 10 ​  , and hence is negative.

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