Linear Inequations-11

From Homeworkwiki

Jump to: navigation, search

Solve 1 ≤ |x - 2| ≤ 3

Solution: We know that:

a ≤ |x - c| ≤ b.

<=> x ∈ [-b + c, -a + c] U [a + c, b + c]

Therefore, 1 ≤ |x - 2| ≤ 3 <=> x ∈ [-3 + 2, -1 + 2] U [1 + 2, 3 + 2]

<=> x ∈ [-1, 1] U [3, 5]

Hence, the solution set of the given inequation is [-1, 1] U [3, 5]

Personal tools
McAfee SECURE sites help keep you safe from identity theft, credit card fraud, spyware, spam, viruses and online scams