Out of four given inequalities the correct inequality is -|-7| > -|-10|
<u>Solution:</u>
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
<em><u>Option 1:</u></em>
-|-4| > |-3|
|-4| = 4, So - |-4| = -4
And |-3| = 3
As -4 cannot be greater than 3
Hence inequality -|-4| > |-3| is incorrect.
<em><u>Option 2:</u></em>
-|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.
<em><u>Option 3:</u></em>
|-9| > |-12|
|-9| = 9 and |-12| = 12
As 9 cannot be greater than 12
Hence inequality |-9| > |-12| is incorrect.
<em><u>Option 4:</u></em>
-|-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.
