Which inequality expresses all the solutions to −4 ≤ 5 − x 5

Solution:

The given inequality is

    −4 ≤ 5 − x ≤ 5

Breaking the inequality into two parts and then Combining Constants with constants in the inequality

⇒ -4 ≤ 5 -x    ∧         5-x ≤5

⇒ -4 -5 ≤ -x     ∧      -x ≤ 5-5

⇒ -9 ≤ -x      ∧       -x ≤ 0        (1)

⇒ Keep in mind , if , -a ≤ -b

then , if negative sign is removed , the inequality changes to

→ a ≥ b

Expression (1) Becomes

→  x  ≤  9          ∧    → x ≥ 0

The solution set of given inequality  −4 ≤ 5 − x ≤ 5  is [ 0 , 9]