The point (0, 0) is a solution to which of these inequalities?
a. y + 5 < 3x – 4
b. y + 5 < 3x + 4
c. y – 4 < 3x – 5
d. y – 5 < 3x – 4

D. y – 5 < 3x – 4

Step-by-step explanation:

When you replace a point in an inequality, and that point is a solution of it, the inequality must remain true.

Let's replace the (0,0) on each inequality and see where does this happen.

In each inequality, we will replace the x and the y with a 0.

A.  y + 5 < 3x – 4

0 + 5 < 3*0 - 4

5 < 0 - 4

5 < -4

That's not true because a negative number can't be greater than a positive one.

B.  y + 5 < 3x + 4

0 + 5 < 3*0 + 4

5 < 4

False, 5 is greater than 4.

C.  y – 4 < 3x – 5

0 - 4 < 3*0 - 5

-4 < -5

If we multiply by -1 on both sides, we need to change the direction of the inequality

4 > 5

False.

D.  y – 5 < 3x – 4

0 - 5 < 3*0 - 4

-5 < -4

5 > 4

True.

Therefore, the point (0,0) is a solution of D.

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