Which of the following inequalities is true for all real values of x?

H

happiness

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What did I do wrong in my work? How is x<= 3/2? This is for the answer D.)

Video: https://youtu.be/-yjkE_IIiZY (skip to 7:43) Also whats the difference between solving and simplifying an inequalitie as mentioned in the video? Thanks.
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There is a mistake on every line of your work.

The square of (x - 2) is not x^2 + 4. As stated in the video, use "FOIL".

You dropped the factor of 3 on the left entirely.

You correctly added 3 to both sides, but then you divided only one term on the left by 3, not the entire expression.

Try again, being careful at those points, and show us your work again if needed.
 
Dr.Peterson said:
There is a mistake on every line of your work.

The square of (x - 2) is not x^2 + 4. As stated in the video, use "FOIL".

You dropped the factor of 3 on the left entirely.

You correctly added 3 to both sides, but then you divided only one term on the left by 3, not the entire expression.

Try again, being careful at those points, and show us your work again if needed.
Click to expand...
Can you show me step-by-step how she got x<= 3/2? I still didn't get it.
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First off I recommend solving the related equality before dealing with the inequality.

\(\displaystyle 3(x - 2)^2 = 3x - 2 \implies 3(x - 2)(x - 2) = 3x - 2 \implies\)

\(\displaystyle 3\{x(x - 2) - 2(x - 2)\} = 3x - 2 \implies WHAT?\)
 
You copied the problem wrong this time; otherwise your work was pretty good as far as you got. You dropped the exponent on the right, which ends up producing a very difficult inequality to solve. When you solve the right problem, it's easy!

With that correction, your work is what I would do up to this:

\(\displaystyle 3x^2 - 12x + 12 \ge 3x^2 - 2\)

I would collect all terms on the left, as in solving a quadratic equation, before doing anything else. You will find that, because of the correction I've made, the problem is much easier now! It will turn into a linear equation.
 
happiness said:
I said it in the original post : "skip to 7:43"
Click to expand...
I didn't hear anything at that point talking about "the difference between solving and simplifying an inequality as mentioned in the video".

I'm glad that everything worked out for you. Cheers :cool:
 
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