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]