Question

If (x) is an integer and it satisfies the inequalities (7y < 49) and (3y ≥ -9), find all the possible values of (y).

A) (y ∈ -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6)
B) (y ∈ -4, -3, -2, -1, 0, 1, 2, 3, 4, 5)
C) (y ∈ -4, -3, -2, -1, 0, 1, 2, 3, 4)
D) (y ∈ -3, -2, -1, 0, 1, 2, 3, 4)

Answer 1

The possible integer values for y that satisfy both inequalities 7y < 49 and 3y ≥ -9 are -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, corresponding to Option B.

Step-by-step explanation:

To find all the possible values of y that satisfy the inequalities 7y < 49 and 3y ≥ -9, we must solve each inequality separately and then find the intersection of the two solution sets, since y must satisfy both inequalities simultaneously.

For the first inequality:

1. Divide both sides by 7: y < 49 / 7
2. Simplify: y < 7

For the second inequality:

1. Divide both sides by 3: y ≥ -9 / 3
2. Simplify: y ≥ -3

Now, we take the intersection of y < 7 and y ≥ -3, which yields all integer values y such that -3 ≤ y < 7. These values are -3, -2, -1, 0, 1, 2, 3, 4, 5, 6. Therefore, the correct answer that includes all possible values of y is:

Option B) y ∈ -3, -2, -1, 0, 1, 2, 3, 4, 5, 6