Question

The point (0,0) is a solution to which of these inequalities?

y+7<2x-6
y-7<2x-6
y+7<2x+6
y-6<2x-7

Answer 1

To determine which of the inequalities has the point (0,0) as a solution, we can substitute \( x = 0 \) and \( y = 0 \) into each inequality and see if it holds true.

1. For the inequality \( y + 7 < 2x - 6 \):
\[
0 + 7 < 2(0) - 6 \implies 7 < -6 \quad \text{(false)}
\]

2. For the inequality \( y - 7 < 2x - 6 \):
\[
0 - 7 < 2(0) - 6 \implies -7 < -6 \quad \text{(true)}
\]

3. For the inequality \( y + 7 < 2x + 6 \):
\[
0 + 7 < 2(0) + 6 \implies 7 < 6 \quad \text{(false)}
\]

4. For the inequality \( y - 6 < 2x - 7 \):
\[
0 - 6 < 2(0) - 7 \implies -6 < -7 \quad \text{(false)}
\]

The only inequality that holds true for the point (0,0) is:

\[
\boxed{y - 7 < 2x - 6}
\]