Solve the inequality. Graph the solution set and write it using interval notation. $| x + 3 | \geq 9$
A) $x \in ( - 12,6 )$;
B) $x \in ( - \infty , 6 ]$;
C) $x \in ( - 12 , \infty )$;
D) $x \in ( - \infty , - 12 ] \cup [ 6 , \infty )$;
E) no solution;

Question

Solve the inequality. Graph the solution set and write it using interval notation. $| x + 3 | \geq 9$
A) $x \in ( - 12,6 )$; 
B) $x \in ( - \infty , 6 ]$; 
C) $x \in ( - 12 , \infty )$; 
D) $x \in ( - \infty , - 12 ] \cup [ 6 , \infty )$; 
E) no solution;

Quizplus · Accepted Answer

We start by isolating the absolute value expression: 
$$|x + 3| \geq 9$$
$$x+3 \leq -9 \text{  or  } x+3 \geq 9$$
Solving for x, we get:
$$x \leq -12 \text{  or  } x \geq 6$$
Therefore, the solution set is:
$$x \in (-\infty, -12] \cup [6, \infty)$$
Which matches option D.

Solve the Inequality ∣x+3∣≥9| x + 3 | \geq 9∣x+3∣≥9 A) x∈(−12,6)x \in ( - 12,6 )x∈(−12,6)

Solve the Inequality $| x + 3 | \geq 9$ A) $x \in ( - 12,6 )$