Solve the inequality. $| x - 4 | - 2 \geq 6$
A) $-$ 4, 12
B) $( - \infty , - 4 ] \cup [ 12 , \infty )$
C) $[ - 4,4 ) \cup ( 4,12 ]$
D) $\phi$

Question

Quizplus · Accepted Answer

Starting from the left side of the inequality:

$|x-4| -2 \geq 6$

$|x-4| \geq 8$

Now we can split this into two inequalities:

$x-4\geq 8 \quad 	ext{OR} \quad x-4\leq -8$

$x\geq 12 \quad 	ext{OR} \quad x\leq -4$

Therefore, the solution set is $\boxed{(-\infty, -4] \cup [12, \infty)}$.

Solve the Inequality ∣x−4∣−2≥6| x - 4 | - 2 \geq 6∣x−4∣−2≥6