Question

Solve the inequality with absolute value
$|x-1|\ge 2$

• A. no solutions
• B. $[3,+\infty )$
• C. $(-\infty ,-1]\cup [3,+\infty )$
• D. $(-\infty ,-1]$
• E. $(-\infty ,+\infty )$

Answer 1

The correct option is C $(-\infty ,-1]\cup [3,+\infty )$

Since $|x|=x$ and $-x$

Therefore, $|x-1|>=2$ may be calculated as:

$x-1>=2$ and $-(x-1)>=2$

$\Rightarrow x>=2+1$ and $-x+1>=2$

$\Rightarrow x>=3$ and $-x>=2-1$

$\Rightarrow x>=3$ and $-x>=1$

$\Rightarrow x>=3$ and $x<=-1$

Therefore, $x$ lies between $(-\infty ,-1]\cup [3,+\infty )$.

Hence, option C is correct.