Question

Which ordered pair is in the solution set of 8x + 16y > 32?

Answer 1

To determine which ordered pair is in the solution set of the inequality \( 8x + 16y > 32 \), we can first simplify the inequality.

Dividing the entire inequality by 8, we get:

\[
x + 2y > 4
\]

Now, we can test a few ordered pairs to see if they satisfy this inequality. Here are some examples of ordered pairs you might want to test:

1. \( (0, 0) \)
2. \( (2, 1) \)
3. \( (1, 2) \)
4. \( (3, 0) \)

Let's check each one.

1. For \( (0, 0) \):
\[
0 + 2(0) > 4 \quad \Rightarrow \quad 0 > 4 \quad \text{(false)}
\]

2. For \( (2, 1) \):
\[
2 + 2(1) > 4 \quad \Rightarrow \quad 2 + 2 > 4 \quad \Rightarrow \quad 4 > 4 \quad \text{(false)}
\]

3. For \( (1, 2) \):
\[
1 + 2(2) > 4 \quad \Rightarrow \quad 1 + 4 > 4 \quad \Rightarrow \quad 5 > 4 \quad \text{(true)}
\]

4. For \( (3, 0) \):
\[
3 + 2(0) > 4 \quad \Rightarrow \quad 3 > 4 \quad \text{(false)}
\]

Based on the tests above, the ordered pair \( (1, 2) \) satisfies the inequality \( 8x + 16y > 32 \).

Thus, the ordered pair \( (1, 2) \) is in the solution set of the inequality.