Answer :

Given:


|5 – 2x| ≤ 3, x ϵ R.


5 – 2x ≥ - 3 or 5 – 2x ≤ 3


5 – 2x ≥ -3


Subtracting 5 from both the sides in the above equation


5 – 2x – 5 ≥ - 3 – 5


-2x ≥ - 8


Now, multiplying by -1 on both the sides in the above equation


-2x(-1) ≥ -8(-1)


2x ≤ 8


Now dividing by 2 on both the sides in the above equation



x ≤ 4


5 – 2x ≤ 3


Subtracting 5 from both the sides in the above equation


5 – 2x – 5 ≤ 3 – 5


-2x ≤ -2


Now, multiplying by -1 on both the sides in the above equation


-2x(-1) ≤ -2(-1)


2x ≥ 2


Now dividing by 2 on both the sides in the above equation



x ≥ 1


Therefore,


x є [1, 4]


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