Question

solve the equation. check for extraneous solutions. will fan and medal

Answer 1

\[9\left| 9-8x \right|=2x+3\]

Answer 2

well, you will get two results:
\(9\left| 9-8x \right|=2x+3\)

\(9(9-8x )=2x+3\) OR \(9(9-8x )=-2x-3\)

Answer 3

solve each case individually.

Answer 4

i dont know where to start. will you walk me through it?

Answer 5

well, expand the right side in case 1

Answer 6

I mean the left side (not the right side)

Answer 7

would you move the x to the left side first?

Answer 8

\(9(9-8x )=2x+3\)
\(9\cdot9-9\cdot8x =2x+3\)
\(81-72x =2x+3\)

Answer 9

So in case two you would have the same, but the right side would be -2x-3

Answer 10

Solve for each:

\(81-72x =2x+3\) \(81-72x =-2x-3\)

Answer 11

x would go on the left side?

Answer 12

you can add 72x to both sides in case 2 and case 1

Answer 13

leaving us with 81=74x+3

Answer 14

two cases:

\(81-72x =2x+3\)
\(81-72x+72x =2x+72x+3\)
\(81=74x+3\)

right!

Answer 15

then subtract 3 from both sides.

Answer 16

78=74x?

Answer 17

yes, so x=?

Answer 18

74/78?

Answer 19

yes

Answer 20

what about in the second case?

Answer 21

Now in case 2:

\(81-72x =-2x-3\)

Answer 22

you also add 72x to both sides,
THEN, add 3 to both sides

Answer 23

x=70/84?

Answer 24

oh the first one is incorrect, and this one too

Answer 25

noooo

Answer 26

when in case one you have:
78=74x

you divide by 74 on both sides, and thus
x=78/74 (not 74/78)

Answer 27

And in case two you made the same mistake

Answer 28

so it would be 84/70?

Answer 29

Yes, for case 2.

Answer 30

And they are not extraneous.

Answer 31

let me say correctly what would have been extraneous:

Answer 32

Any x-solution, in this case, that is equal to \(C\) that satisfies:
\(C<-2/3\)

Answer 33

because if x is less than -2/3
then 2x+3 is negative, and absolute value can NOT e equal to negative
(since absolute value is really a distance)