for each inequality tell whether the given value is a solution. a.x+8 > 15 x=4 b. 6x __<_ 30 x= -8 c. 4y-7<12 y=-1 d. z+2 _>__4+3z z=2

I'll do the first one. x+8>15

You want to get the letters on one side and numbers on the other. Subtract 8 from both sides.
x>7

a. For the inequality x+8 > 15, let's substitute x=4:

4 + 8 > 15
12 > 15

Since 12 is not greater than 15, the given value x=4 is not a solution to the inequality.

b. For the inequality 6x ≤ 30, let's substitute x=-8:
6(-8) ≤ 30
-48 ≤ 30

Since -48 is less than or equal to 30, the given value x=-8 is a solution to the inequality.

c. For the inequality 4y-7 < 12, let's substitute y=-1:
4(-1) - 7 < 12
-4 - 7 < 12
-11 < 12

Since -11 is less than 12, the given value y=-1 is a solution to the inequality.

d. For the inequality z+2 ≥ 4+3z, let's substitute z=2:
2 + 2 ≥ 4 + 3(2)
4 ≥ 4 + 6
4 ≥ 10

Since 4 is not greater than or equal to 10, the given value z=2 is not a solution to the inequality.

To determine if a given value is a solution for an inequality, we substitute the value into the inequality and check if it results in a true statement. Let's go through each inequality:

a. x + 8 > 15, with x = 4
Substitute x with 4:
4 + 8 > 15
12 > 15
This statement is False. 12 is not greater than 15.
Therefore, x = 4 is not a solution to the inequality x + 8 > 15.

b. 6x ≤ 30, with x = -8
Substitute x with -8:
6(-8) ≤ 30
-48 ≤ 30
This statement is True. -48 is less than or equal to 30.
Therefore, x = -8 is a solution to the inequality 6x ≤ 30.

c. 4y - 7 < 12, with y = -1
Substitute y with -1:
4(-1) - 7 < 12
-4 - 7 < 12
-11 < 12
This statement is True. -11 is less than 12.
Therefore, y = -1 is a solution to the inequality 4y - 7 < 12.

d. z + 2 ≥ 4 + 3z, with z = 2
Substitute z with 2:
2 + 2 ≥ 4 + 3(2)
4 ≥ 4 + 6
4 ≥ 10
This statement is False. 4 is not greater than or equal to 10.
Therefore, z = 2 is not a solution to the inequality z + 2 ≥ 4 + 3z.

In summary:
a. x = 4 is not a solution.
b. x = -8 is a solution.
c. y = -1 is a solution.
d. z = 2 is not a solution.