Question

19. Solve the equation. Check for extraneous solutions. 9|9-8x| = 2x + 3

Answer 1

Rock is already replying so you don't need me ;)

Answer 2

you need to solve two things

\(9-8x=\dfrac{2x+3}{9}\)

and

\(9-8x=-(\dfrac{2x+3}{9})\)

Answer 3

@zzr0ck3r Aren't you able to graph it as well? Curious, I found the two values myself, wanted to see if my method worked as well with your final answer at the end.

Answer 4

\(|f(x)|=a\implies f(x)=a \text{ and } f(x) =-a\)

Answer 5

Ohhh. That immediately explains why I keep getting it wrong, tbh

Answer 6

You can graph it but it is going to be hard to tell where they intersect unless it is a nice number, and it is not.

Answer 7

Working out just fine for you, deercult?

Answer 8

Eh, no. I'm miserable with math, I think now I'm just messing up the order of equations, though?
But in general, I doubt 0.185... is supposed to be an answer.

I tried to work it out like this:
9 - 8x = (2x+3)/9
6 - 8x = 2x / 9
54 - 8x = 2x
54 = 10x
And I think I'm gonna try and redo it again. Rah.

Answer 9

I don't see why you did -3 first.

Answer 10

I did my graphing method and already have both x values, but let me try this method he showed:

Answer 11

Oh. I got PEMDAS backwards, incredible

Answer 12

9 - 8x = (2x + 3 ) / 9 multiply by 9
81 - 72x = 2x + 3 (add 72x)
81 = 74x + 3 (subtract 3)
78 = 74x (divide by 74)
78/74 = x
x = ?

Answer 13

This one is the 39/37 value I found graphing. 1/2 of the values in this situation, but equal the same decimal.

Answer 14

Can calculate x for me in this case?

Answer 15

Well, in that case, I got another repeating decimal, '1.054...'

Answer 16

Yes, correct.

Answer 17

Alright, then, I've got it written down. Awful tired of repeating decimals, tbh.

Sooo, for th' second one..
9-8x = -((2x + 3)/9)
Yeh? Or just -(2x + 3)/9, I suppose?

Answer 18

9-8x = -((2x + 3)/9) is correct.

Answer 19

Work it out, and tell me what you get?

Answer 20

Alright, then...
9-8x = -2x - 3 / -9 eh? And goin' on,
-81+72x = -2x - 3
-81 = -74x - 3
-78 = -74x
Which just gets an even worse repeating decimal, '0.948717...'

Answer 21

Hmm, I got 1.20, not a repeating decimal.

Answer 22

I did somethin' wrong along the way then, since even (-78)/(-74) is '1.054...' accordin' to my calculator. Crud.

Answer 23

Do you mind if I do a proof instead this time?

Answer 24

Not at all.

Answer 25

Okay, the original is: 9l9-8xl= 2x + 3
My method was graphing, and I found the value where they intersected, so. Let's see if my value of 1.20 is correct for the x value.

Answer 26

9l9-8(1.2)l = 2(1.2) + 3
9l9-9.6l= 2.4 + 3
9l-.06l = 5.4
(mod it - absolute value)
9 * 0.6 = 5.4
5.4 = 5.4

Answer 27

Oops,
9l-0.6l = 5.4*****

Answer 28

I see!

Answer 29

So, this result in the value of 1.054 (repeating .054) and 1.20 to be the x values, you may also do a proof for the 1.054 and you will get 5.10.... = 5.10...... I already did all the work, so both do work in this case.

Answer 30

results*

Answer 31

Ah, nice! Thanks, then.

Answer 32

Of course, anytime. If you need any further explanation on anything, please ask.