solve the following absolute value inequality. |x - 3| > 7 x > ? x <

Explanation:

Step1: Split the absolute - value inequality

For (|a|>b) ((b > 0)), it is equivalent to (a>b) or (a < - b). Here (a=x - 3) and (b = 7), so (x-3>7) or (x - 3<-7).

Step2: Solve (x-3>7)

Add 3 to both sides of the inequality (x-3>7). We get (x-3 + 3>7+3), which simplifies to (x>10).

Step3: Solve (x - 3<-7)

Add 3 to both sides of the inequality (x - 3<-7). We get (x-3+3<-7 + 3), which simplifies to (x<-4).

Answer:

(x>10), (x<-4)