Question

What is the solution set for StartAbsoluteValue z + 4 EndAbsoluteValue greater-than 15? 11 less-than z less-than 19 Negative 19 less than z less-than 11 z less-than negative 19 or z greater-than 11 z less-than 19 or z greater-than 11

Answer 1

z less-than negative 19 or z greater-than 11

Explanation:

Answer 2

z less-than negative 19 or z greater-than 11

Explanation:

Given the inequality
`|z+4|>15`, we are to find the solution set of the inequality. Since the the function is an absolute value, this means that the function will be positive and negative.

For the positive value of the function;

`z+4>15\\\\subtract\ 4\ from \ both \ sides\\z+4-4 > 15 -4\\\\z>11`

For the negative value of the function we have;

`-(z+4) > 15\\\\-z-4> 15\\add\ 4 \ to\ both \ sides\\\\-z-4+4> 15+4\\\\-z> 19\\\\`

Multiplying both sides of the inequality by -1 will change the sense of the inequality sign;'

`-(-z)< -19\\\\z<-19`

Hence the solution sets are
`z> 11 \ and \ z< -19 \\` OR z less-than negative 19 or z greater-than 11