is Khan academy wrong

[Ben fennell]

I don’t think khan academy is wrong is it
i just Keep getting the same answer 4/3 < x > 2

 

[JeffM]

Hmm

Suppose the question was: Find where it is true that

[MATH]3x - 91 > - 87 \implies 3x > 91 - 87 = 4 \implies x > \dfrac{4}{3}.[/MATH]
Do you buy that?

Suppose the question was: Find where it is true that

[MATH]21x - 17 > 25 \implies 21x > 17 + 25 = 42 \implies x > 2.[/MATH]
Do you buy that?

But your problem does not ask that simple question, does it?

Let's think about 5.

[MATH]3 * 5 - 91 = 15 - 91 = - 76 > - 87.[/MATH]
True. With me to here?

[MATH]21 * 3 - 17 = 63 - 17 = 46 > 42.[/MATH] True.

Still with me?

So 5 satisfies both conditions but it is outside 4/3 < x < 2. So restricting x to that range cannot be correct, right?

Let's think about 3/2.

[MATH]3 * \dfrac{3}{2} - 91 = \dfrac{9}{2} - \dfrac{182}{2} = - \dfrac{173}{2} > - \dfrac{174}{2} = - 87.[/MATH]
3/2 DOES meet that condition. How about the other?.

[MATH]21 * \dfrac{3}{2} - 17 = \dfrac{63}{2} - \dfrac{17}{2} = \dfrac{46}{2} = 23 \not > 25.[/MATH]
3/2 DOES NOT meet that condition.

But no one said that a number had to meet BOTH conditions. It can meet either condition. And 3/2 meets one of them.

This is really a question about what "or" means. Want to take another go at this problem?

 

[Dr.Peterson]

I don’t think khan academy is wrong is it
i just Keep getting the same answer 4/3 < x > 2

Do you see that your answer, 4/3 < x > 2, is not the same as their answer (c), 4/3 < x < 2?

What you wrote means that x > 4/3, AND x > 2. If that were true, then any number that is greater than 2 is also greater than 4/3, so you can simplify it to x > 2.

But the question has an OR in it, so your answer has to, as well. It should be x > 4/3, OR x > 2. This, too, can be simplified. It's easiest to see this by putting x > 4/3 and x > 2 separately on a number line, and thinking about which numbers are in at least one of these sets, which is what "or" means. What do you get?

You were right, except that you used the wrong conjunction, and didn't think about its implications.

 

[Ben fennell]

Thinks you very much that was really helpful