Question

Select all values for y that belong to the solution set of the following compound inequality. −4y + 9 > 37 or 3y − 11 ≥ −17 Select one or more: A. 4 B. 0 C. -2 D. -5 E. 6 F. -13

Answer 1

Answer:

A. 4

B. 0

C. -2

E. 6

F. -13

Step-by-step explanation:

step 1

Solve the inequality A

we have

$-4y+9 > 37$ ----> inequality A

Multiply by -1 both sides

$4y-9 < -37$

Adds 9 both sides

$4y < -37+9$

$4y < -28$

Divide by 4 both sides

$y < -7$

The solution of the inequality A is the interval (-∞,-7)

step 2

Solve the inequality B

we have

$3y-11\geq -17$ ----> inequality B

Adds 11 both sides

$3y\geq -17+11$

$3y\geq -6$

Divide by 3 both sides

$y\geq -2$

The solution of the inequality B is the interval [-2,∞)

step 3

Find the solution of the system of inequalities

inequality A or inequality B

The solution is

(-∞,-7) ∪ [-2,∞)

If a value of y is a solution of the compound inequality, then the value must lie on any of the two intervals of the solution

Verify all values

case A) 4

The value of y lie on the interval [-2,∞)

therefore

4 belong to the solution set

case B) 0

The value of y lie on the interval [-2,∞)

therefore

0 belong to the solution set

case C) -2

The value of y lie on the interval [-2,∞)

therefore

-2 belong to the solution set

case D) -5

The value of y not lie on the interval (-∞,-7) and not lie on the interval [-2,∞)

therefore

-5 belong to the solution set

case E) 6

The value of y lie on the interval [-2,∞)

therefore

6 belong to the solution set

case F) -13

The value of y lie on the interval (-∞,-7)

therefore

-13 belong to the solution set