Question

Which value for x makes the open sentence true?



10 • 8 – 3x + x2 ≥ x3 + x2



A.


6


B.


4


C.
5


D.


7

Answer 1

@mathmale

Answer 2

Hello, and good morning! Why don't we approach this problem by actually solving it?
10 • 8 – 3x + x2 ≥ x3 + x2 would be better written as 10 • 8 – 3x + x^2 ≥ x^3 + x^2, or \[10 • 8 – 3x + x^2 ≥ x^3 + x^2\]

Answer 3

Keep in mind that there are rules about what we do first, called "Order of Operations" rules. Those rules say we must multiply and divide before we add or subtract.

Thus, we have to multiply 10 and 8 first. We get:\[80 – 3x + x^2 ≥ x^3 + x^2\]

Answer 4

We could now simplify this inequality by subtracting x^2 (x squared) from both sides. Would you try doing that, please?

Answer 5

yea hold on im like taking notes lol

Answer 6

wait how would I subtract x^2 and 80

Answer 7

Editorial comment: The chances are that you haven't yet learned how to solve equations involving x^3, so (for now, at least), don't bother. Instead, take \[80 – 3x + x^2 ≥ x^3 + x^2\] and cross out the x^2 term on both sides, leaving

Answer 8

\[80 – 3x ≥ x^3 \]

Answer 9

no i haven't learned this and okay thank you

Answer 10

Now substitute each of the possible answer choices into this inequality until you find the one that makes this inequality "true." Your choices are 6, 4, 5, 7.

Answer 11

Choose one of those at random.

Answer 12

For example, let's try x=5.
Substituting that into \[80 – 3x ≥ x^3, ~we~get~ 80 – 3(5) ≥ (5)^3\]

Answer 13

Please do the math here. Multiply 3 times 5. Find the cube of 5. Substitute those values into the inequality. Can you do this comfortably?

Answer 14

@sierraleone17 : Please respond; I need to know that you're involved in this discussion. OpenStudy indicates that you're looking at a different math problem elsewhere.

Answer 15

ohh i got b

Answer 16

Would you please show me how you got "b"?

Answer 17

I'd like to see your math.

Answer 18

idek how to put it up here and i didnt really understand so i just did my best guess

Answer 19

that's what I was afraid of. Let's do the math, please.\[80 – 3x ≥ x^3, ~we~get~ 80 – 3(5) ≥ (5)^3.\] Earlier I asked you to evaluate 3(5) and (5)^3. Please do that now.

Answer 20

15 and 125

Answer 21

right. Is 80-15 greater than or equal to 125? If yes, you have your answer. If no, you don't, and must try another one of the four possible answer choices. Please proceed until you have identified the correct answer.

Answer 22

no it isnt and okay

Answer 23

Let me know when you're finished and believe you have the correct answer.

Answer 24

okay

Answer 25

:) thank you!!!

Answer 26

is it b?

Answer 27

I'd really prefer that you show your actual work, rather than asking, "Is it b?"

\[80 – 3x ≥ x^3, ~we~get~ 80 – 3(4) ≥ (4)^3~when~x=4\] Would you evaluate that, please?

Answer 28

yea thats what is did i got 12 and 64

Answer 29

Fine; you must now substitute those back into the inquality:\[80 – 3x ≥ x^3, ~we~get~ 80 – (12) ≥ 64\] Is this inequality true or false?

Answer 30

false?