Q. Solve the inequality |x + 3a| 2|x − 2a|, where a is a positive constant.

I managed to turn it into the quadratic form, 3x^2 - 22ax + 7a^2 0, but am not able to find the x values. Please help.

Question

Q. Solve the inequality |x + 3a| > 2|x − 2a|, where a is a positive constant.

I managed to turn it into the quadratic form, 3x^2 - 22ax + 7a^2 > 0, but am not able to find the x values. Please help.

myininaya · Answer

How did you get that that was greater than O?

myininaya · Answer

I think that direction of the inequality is wrong.
But you can factor your expression to the left of the inequality.

anonymous · Answer

I first squared both sides, opened the brackets & rearranged them..

Oh- could u pls show me how?

myininaya · Answer

Yes. I know about the squaring part. I'm just saying I don't agree with your direction of the inequality.

You factor it just like you would factor any other quadratic that can be factored over the integers.
Find two factors of a*c that have product ac and sum b.
Find two factors of 7(3) that have product 7(3) and sum -22.

anonymous · Answer

Ok, I'll try it, Thanks :)