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

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.