Question

Which of the following is the solution to 9|x+4|>54 ?

Answer 1

Answer:

x < -10, x > 2

Step-by-step explanation:

9|x+4| > 54

|x+4| > 6

Split the absolute value into two equation, positive and negative.

1.)POSITIVE

x+4 > 6

x > 2

2.)NEGATIVE

-(x+4) > 6

-x - 4 > 6

-x > 10

x < -10

Answer 2

Answer:

$\large\boxed{x<-10\ \vee\ x>2\to x\in(-\infty,\ -10)\ \cup\ (2,\ \infty)}$

Step-by-step explanation:

$9|x+4|>54\qquad\text{divide both sides by 9}\\\\\dfrac{9|x+4|}{9}>\dfrac{54}{9}\\\\|x+4|>6\iff x+4>6\ \vee\ x+4<-6\\\\x+4>6\qquad\text{subtract 4 from both sides}\\\\x+4-4>6-4\\\\x>2\\\\x+4<-6\qquad\text{subtract 4 from both sides}\\\\x+4-4<-6-4\\\\x<-10$