Solve the inequality. $| 9 x + 9 | \geq 63$
A) $[ - 6,1 ] \cup [ 1,8 ]$
B) $( - \infty , - 8 ] \cup [ 6 , \infty )$
C) $( - 7 , - 1 ] \cup [ 1,7 )$
D) $\phi$

Question

Quizplus · Accepted Answer

We can first isolate the absolute value by dividing both sides of the inequality by 9:
$$|9x+9|\geq 63 \Rightarrow |x+1|\geq 7$$
Then we can split the inequality into two cases: $x+1\geq 0$ and $x+1<0$.

For $x+1\geq 0$ (or $x\geq -1$), we have:
$$|x+1|\geq 7 \Rightarrow x+1\geq 7 	ext{  or  } x+1\leq -7 \Rightarrow x\geq 6 	ext{  or  } x\leq -8$$

For $x+1<0$ (or $x<-1$), we have:
$$|x+1|\geq 7 \Rightarrow -(x+1)\geq 7 	ext{  or  } -(x+1)\leq -7 \Rightarrow x\leq -8 	ext{  or  } x\geq 6$$

Therefore, the solution is:
$$x\in(-\infty,-8]\cup[6,\infty)$$
which corresponds to choice (B).

Solve the Inequality ∣9x+9∣≥63| 9 x + 9 | \geq 63∣9x+9∣≥63

Solve the Inequality $| 9 x + 9 | \geq 63$