Write the solution set of values of x satisfying -x-1- - 3 and -x-1- - 1

|x 1|≤ 3 ⇔ 1 3≤ x≤ 1+3 ⇔ 2≤ x≤ 4 ⇔ xϵ [ 2,4] |x 1|≥ 1 ⇔ x≤ 1 1 or x≥ 1+1 ⇔ x≤ 0 or x≥ 2 ⇔ x ϵ ( ∞ ,0] or x ϵ [2,∞ ) x ϵ ( ∞ ,0] ∪ [2,∞ ) Hence,the solution se ...

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Standard XII

Mathematics

Inequalities Involving Modulus Function

Write the sol...

Question

Write the solution set of values of x satisfying $| x - 1 | \leq 3 a n d | x - 1 | \leq 1$ .

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Solution

$| x - 1 | \leq 3 \Leftrightarrow 1 - 3 \leq x \leq 1 + 3 \Leftrightarrow - 2 \leq x \leq 4 \Leftrightarrow x ϵ [- 2, 4] | x - 1 | \geq 1 \Leftrightarrow x \leq 1 - 1 o r x \geq 1 + 1 \Leftrightarrow x \leq 0 o r x \geq 2 \Leftrightarrow x ϵ (- \infty, 0] o r x ϵ [2, \infty) x ϵ (- \infty, 0] \cup [2, \infty)$

Hence,the solution set of the given system of inequations is $[- 2, 0] \cup [2, 4]$

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Write the solution set of values of x satisfying |x−1|≤3 and |x−1|≤1.

|x−1|≤3⇔1−3≤x≤1+3⇔−2≤x≤4⇔xϵ[−2,4]|x−1|≥1⇔x≤1−1 or x≥1+1⇔x≤0 or x≥2⇔x ϵ (−∞,0] or x ϵ [2,∞)x ϵ (−∞,0] ∪[2,∞) Hence,the solution set of the given system of inequations is [−2,0]∪[2,4]

Write the solution set of values of x satisfying $| x - 1 | \leq 3 a n d | x - 1 | \leq 1$ .