Question

Which inequality has -12 in its solution set?

Answer 1

Answer:

Option D. $x+5\leq -4$

Step-by-step explanation:

Verify each case

case A) we have

$x+6< -8$

Solve for x

Subtract 6 both sides

$x< -8-6$

$x< -14$

The solution is the interval -----> (-∞,-14)

therefore

This inequality does not have -12 in its solution

case B) we have

$x+4\geq -6$

Solve for x

Subtract 4 both sides

$x\geq -6-4$

$x\geq -10$

The solution is the interval -----> (-10,∞)

therefore

This inequality does not have -12 in its solution

case C) we have

$x-3 > -10$

Solve for x

Adds 3 both sides

$x > -10+3$

$x > -7$

The solution is the interval -----> (-7,∞)

therefore

This inequality does not have -12 in its solution

case D) we have

$x+5\leq -4$

Solve for x

Subtract 5 both sides

$x\leq -4-5$

$x\leq -9$

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

therefore

This inequality has -12 in its solution