Question

Which of the following inequalities is correct? -|-4| > |-3| -|1| < -|-5| |-9| > |-12| -|-7| > -|-10|

Answer 1

Out of four given inequalities the correct inequality is -|-7| > -|-10|

Solution:

Need to determine which of the given inequality is/are correct from given four options.

lets first understand what is mod of any real number "x" that is |x| means.

|x| = |-x| = absolute value of x ignoring its sign = x

let’s check each option

Option 1:

-|-4| > |-3|  

|-4| = 4, So - |-4| = -4

And |-3|  = 3

As -4 cannot be greater than 3

Hence inequality -|-4| > |-3| is incorrect.

Option 2:

-|1| < -|-5|  

|1| = 1, so - |1| = -1 and |-5| = 5, so -|-5|   = -5

As -1 cannot be less than -5 (negative sign)

Hence inequality -|1| < -|-5| is incorrect.

Option 3:

|-9| > |-12|  

|-9| = 9 and |-12| = 12  

As 9 cannot be greater than 12  

Hence inequality |-9| > |-12| is incorrect.

Option 4:

-|-7| > -|-10|

|-7| = 7, so - |-7| = -7 and |-10| = 10, so -|-10|   = -10

As -7 is greater that -10 (negative integers).

Hence inequality -|-7| > -|-10| is correct.