Question

Which ordered pair is a solution of the inequality?
y (>=) 4x - 5
A. (3, 4)
B. (2, 1)
C. (3, 0)
D. (1, 1)

Answer 1

Plug in each ordered pair to test

Answer 2

oh okay one moment

Answer 3

For example, let's say you wanted to test the ordered pair (10,5)

x = 10
y = 5

Replace each x with 10, each y with 5

\[\Large y \ge 4x - 5\]
\[\Large 5 \ge 4*10 - 5\]
\[\Large 5 \ge 40 - 5\]
\[\Large 5 \ge 35\]

which is false. So (10,5) is NOT in the solution region. This means (10,5) is NOT a solution to the inequality.

Answer 4

Okay so so far I am on A so would it look like 4 (> =) 4(3) - 5

Answer 5

A is not the one it looks like

Answer 6

no need for parenthesis around the inequality sign

you can say

4 >= 4(3) - 5

Answer 7

4 >= 4(3) - 5 will turn into 4 >= 7 which is false

so yes, A is not part of the solution set

Answer 8

Oh okay

Answer 9

So the next one is 1 >= 4(2) - 5 which is B is not correct because I get 1>=3

Answer 10

good, so B is out too

Answer 11

Okay so let me find out C

Answer 12

So after doing C I get 0 >= 7 which is not right so then it must be D let me check

Answer 13

I think its D is it? I got 1 >= 1

Answer 14

y >= 4x - 5

y >= 4*1 - 5 ... replace x with 1

1 >= 4*1 - 5 ... replace y with 1

1 >= 4 - 5

1 >= -1 .... true

Answer 15

Since 1 >= -1 is true, this means D is the only point in the solution set

Answer 16

I had a feeling it was -1 I was not too sure though haha but actually it makes sense I think because 1 would be greater

Answer 17

So as we can see on the graph (see attached image) the blue shaded region represents the solution set of \(\Large y \ge 4x-5\)

The only point in that solution set is D(1,1). The other points are NOT in the blue shaded region

Answer 18

Oh okay so it is D?

Answer 19

yes D is the only answer

Answer 20

Okay I have a similar one I will re post and then put the answer I think it is and tag you :D. Thanks for the medal :DD