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
\(\frac{2{\text{x}}}{2} \le \frac{8}{2}\)
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
\(\frac{2{\text{x}}}{2} \ge \frac{2}{2}\)
x ≥ 1
Therefore,
x є [1, 4]