Question

The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Check all that apply. $8 $9 $11 $13 $14 $15

Answer 1

x < 9...this is saying the hourly wage is less then 9 (not including 9)
x > = 14...this is saying the hourly wage is 14 and above

so possible values are : 8,14,15 <==

Answer 2

we have

$x<9$ ------> inequality A

The solution of the inequality A is the interval--------> (-∞,9)

All real numbers less than $9$

$x\geq14$ -----> inequality B

The solution of the inequality B is the interval--------> [14,∞)

All real numbers greater than or equal to $14$

The solution Inequality A or Inequality B is equal to

Solution A+Solution B

(-∞,9)U[14,∞)    

The solution of the compound system of inequalities must satisfy inequality A or inequality B

we're going to verify every case

case A) $\ 8$

Substitute the value of x in the inequality A and in the inequality B to verify

Verify inequality A

$8<9$ -------> is true

Therefore

$\ 8$ is a possible value for x

You don't need to check for inequality B

case B) $\ 9$

Substitute the value of x in the inequality A and in the inequality B to verify

Verify inequality A

$9<9$ -------> is not true

Verify inequality B

$9\geq14$ ------> is not true

Therefore

$\ 9$ is not a possible value for x

case C) $\ 11$

Substitute the value of x in the inequality A and in the inequality B to verify

Verify inequality A

$11<9$ -------> is not true

Verify inequality B

$11\geq14$ ------> is not true

Therefore

$\ 11$ is not a possible value for x

case D) $\ 13$

Substitute the value of x in the inequality A and in the inequality B to verify

Verify inequality A

$13<9$ -------> is not true

Verify inequality B

$13\geq14$ ------> is not true

Therefore

$\ 13$ is not a possible value for x

case E) $\ 14$

Substitute the value of x in the inequality A and in the inequality B to verify

Verify inequality A

$14<9$ -------> is not true

Verify inequality B

$14\geq14$ ------> is true

Therefore

$\ 14$ is a possible value for x

case F) $\ 15$

Substitute the value of x in the inequality A and in the inequality B to verify

Verify inequality A

$15<9$ -------> is not true

Verify inequality B

$15\geq14$ ------> is true

Therefore

$\ 15$ is a possible value for x

therefore

the answer is

$\ 8$

$\ 14$

$\ 15$