Inequalities+absolute value

We reverse the sign only when we multiply the inequality by a negative sign.

You see I wrote -2x + 4 < 6 then I solved it as -x < 1.

Now since I need x instead of -x , I multiplied the inequlity with -1, hence the sign of the inequality was reversed and we got x > -1.

I hope it makes sense.

So in this case, we are not multiplying it by -1 but it is already in that form i.e. positive and negative.

Thanks for you reply.

If we read the expression, it means (according to me) that absolute value (i.e. the positive value) of 2x-4 is less than 6.
But when we read the second version, it means that the negative absolute value of -2x+4 is less than 6.


Is it sounding weird or its fine?

yes, that is true. This is how we read it and everything sounds cool.

That's great. Thanks so much for your reply. Because i have read everywhere that ABSOLUTE VALUE can never be negative, that is what caused me trouble in understanding inequalities+absolute value of an expression.

Hi abhimahna

I have the same doubt as I am not able to really understand it after going through various posts and the link you told me about.

|2x-4|<6

It means that the positive value of 2x-4 is less than 6. It means that distance of 2x from 4 is less than 6.

But when we write: -2x+4<6

I am still confused as to why we do not change the sign. This doubt persists because absolute value= positive value and thus the sign would remain the same but when we take the negative value on L.H.S, we are multiplying it by negative 1. And when we multiply or divide by negative 1 we change the sign.

If you don't mind, can you please explain this (below) on a number line so that I understand what exactly is going on here.

|x-4|<6

Means distance of x from 4 is less than 6.

|x+4|<6

Does this also means the same or +/- change how we read this expression?


Looking forward to your reply.

Thanks

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