Question

what is |4x + 9| = 8x - 7

Answer 1

x= 15/4 or -1/6

Answer 2

how so?

Answer 3

i got the -1/6 but i dont know how to get the 15/4

Answer 4

15/4 and -1/6 is not correct answer.


Sorry that I have to type out a lot. Please be patient with me if you want to know how to get answer, lol.


First, we need to split it into two cases: one where \(4x+9\) is positive, and other case where \(4x+9\) is negative.

We need to know what value x can be in these cases.

So let \(4x+9=0\\~\\4x=-9\\~\\x=-\dfrac{9}{4}\)

So we have two cases: \(x<-\dfrac{9}{4}\) and \(x>-\dfrac{9}{4}\)

In case \(x>-\dfrac{9}{4},~4x+9\) is positive,so we can eliminate absolute value, because it won't do anything.

So you have \(4x+9=8x-7\\~~~~~~~~~~~~~\vdots\\~~~~~~~~~x = 4\)

Remember, x have to be greater than \(-\dfrac{9}{4}\) in this case:

\(4>-\dfrac{9}{4}\) True \(\checkmark\)

Now let's looks at other case, one where \(x<-\dfrac{9}{4}\)

We have to add negative sign right next to \((4x+9)\), because we need it to be positive, so double negative will make it positive.

So you have \(-(4x+9)=8x-7\\~~~~~~~~~~~~~~~~~~~~\vdots\\~~~~~~~~~~~~~~~x = -\dfrac{1}{6}\)

Since x need to be smaller than -9/4, x cannot be -1/6 because -1/6 is greater than -4/9

So False

You are left with \(\boxed{x=4}\)

Does that make sense?

Answer 5

@babalaba