Answer:
A. 4
B. 0
C. -2
E. 6
F. -13
Step-by-step explanation:
step 1
Solve the inequality A
we have
[tex]-4y+9 > 37[/tex] ----> inequality A
Multiply by -1 both sides
[tex]4y-9 < -37[/tex]
Adds 9 both sides
[tex]4y < -37+9[/tex]
[tex]4y < -28[/tex]
Divide by 4 both sides
[tex]y < -7[/tex]
The solution of the inequality A is the interval (-∞,-7)
step 2
Solve the inequality B
we have
[tex]3y-11\geq -17[/tex] ----> inequality B
Adds 11 both sides
[tex]3y\geq -17+11[/tex]
[tex]3y\geq -6[/tex]
Divide by 3 both sides
[tex]y\geq -2[/tex]
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
