Question

solve 1≤|x-2|≤3

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Answer 1

I think this should be correct

Answer 2

Answer:

-1 ≤ x ≤ 5

Step-by-step explanation:

Given: 1 ≤ |x - 2|≤3

We know that if x  ≤ y ≤ z then x ≤ y and y ≤ z.

(i)

1 ≤ |x - 2|

⇒ |x - 2| ≥ -1

True for all x.

(ii)

⇒ |x - 2| ≤ 3

We know that if |y| ≤ x then - x ≤ y ≤ x

⇒ -3 ≤ x - 2 ≤ 3

⇒ x - 2 ≥ - 3 and x - 2 ≤ 3

(a)

x - 2 ≥ -3

x ≥ -1

(b)

x - 2 ≤ 3

x ≤ 5

On combining the intervals, we get

x ≥ - 1 and x ≤ 5

Therefore:

Solution : -1 ≤ x ≤ 5

Interval Notation : [-1,5]

Hope it helps!