Q. 325.0( 3 Votes )

Fill in the blank

Answer :

(i) ≤


-4x ≥ 12


Dividing by 4, we get


-x ≥ 3


Now, taking negative both sides inverts the inequality sign


x ≤ 3


(ii)



Multiplying by 4, we get


-3x ≥ -12


Now, taking negative both sides invert the inequality sign


3x ≤ 12


x ≤ 4


(iii) >



Now, for above to be greater than 0,


x + 2 > 0


x > -2


(iv) >


x > -5


Multiplying by 4 both sides, we get


4x > -20


(v) >


x > y


Since, z < 0, i.e. z is negative and multiplying by negative inverts the inequality sign


xz < yz


Now, taking negative both sides invert the inequality sign


-xz > -yz


(vi) >


q < 0


Now, taking negative both sides invert the inequality sign


-q > 0


Adding p both side, we get


p – q > p [since, p>0 inequality sign retains the same]


(vii) <, >


Given,


|x + 2| > 5


there are two cases


x + 2 > 5 and –(x + 2) < 5


x > 3 and –x – 2 < 5


x > 3 and –x > 7


x > 3 and x < -7


[Taking negative both sides invert the inequality sign]


(viii)


-2x + 1 ≥ 9


Adding -1 both side, we get


-2x ≥ 8


x ≤ -4 [Dividing by negative inverts the inequality sign]


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