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

The accepted y-values are:

4, 0, -2, 6 and -13

Explanation:

We are looking for the values that satisfy either the first inequality, the second inequality or both.

Therefore, to get the y-values that belong to the solution set, we will simply substitute with the given values in both inequalities. The ones that satisfy at least one inequality will be accepted. If a value of y does not satisfy any of the two inequalities, then it will be rejected

This is done as follows:

a. At y = 4:

Inequality 1 > -4y + 9 = -4(4) + 9 = -7 which is not greater than 37

Inequality 2 > 3y - 11 = 3(4) - 11 = 1 which is greater than -17

The second inequality is satisfied, therefore, 4 belongs to the solution set

b. At y = 0:

Inequality 1 > -4y + 9 = -4(0) + 9 = 9 which is not greater than 37

Inequality 2 > 3y - 11 = 3(0) - 11 = -11 which is greater than -17

The second inequality is satisfied, therefore, 0 belongs to the solution set

c. At y = -2:

Inequality 1 > -4y + 9 = -4(-2) + 9 = 17 which is not greater than 37

Inequality 2 > 3y - 11 = 3(-2) - 11 = -17 which is equal to -17

The second inequality is satisfied, therefore, -2 belongs to the solution set

d. At y = -5:

Inequality 1 > -4y + 9 = -4(-5) + 9 = 29 which is not greater than 37

Inequality 2 > 3y - 11 = 3(-5) -11 = -26 which is not greater than or equal to 17

Neither of the two inequalities is satisfied, therefore, -5 does not belong to the solution set

e. At y = 6:

Inequality 1 > -4y + 9 = -4(6) + 9 = -15 which is not greater than 37

Inequality 2 > 3y - 11 = 3(6) - 11 = 7 which is greater than -17

The second inequality is satisfied, therefore, 6 belongs to the solution set

f. At y = -13:

Inequality 1 > -4y + 9 = -4(-13) + 9 = 61 which is greater than 37

Inequality 2 > 3y - 11 = 3(-13) - 11 = -50 which is not greater than or equal to -17

The first inequality is satisfied, therefore, -13 belongs to the solution set

Hope this helps :)

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)