Question

$|x-1|+|x+2|\ge 3$, then complete solution set of this inequation is?

• A. $[1,\infty )$
• B. $(-\infty ,-2]$
• C. R
• D. $[-2,1]$

Answer 1

Answer: (A), (B)

$[1,\infty )$
$(-\infty ,-2]$

Consider the inequality, $|x-1|+|x+2|\ge 3$

$⟹x-1+x+2\ge 3$ and $x-1+x+2\le -3$

$⟹2x+1\ge 3$ and $2x+1\le -3$

$⟹2x\ge 3-1$ and $2x\le -3-1$

$⟹2x\ge 2$ and $2x\le -4$

$⟹x\ge 1$ and $x\le -2$

The solution set is,

From $x\ge 1$ we get $[1,\infty )$

From $x\le -2$ we get $(-\infty ,-2]$

Solution : A and B.