Question

Solve the equation. Check for extraneous solutions.

9|9 – 8x| = 2x + 3

Answer 1

I can get to x=39/37 and x=84/70. From there??

Answer 2

I got one of those. I did get x=84/70. But all you need to is to check if both work now. (Also 84/70 can be reduced.)

Answer 3

Yep I got both of those. I made a mistake in adding earlier. My bad.
Just plug them back in and see you get the same thing on both sides.

Answer 4

How do I do that using fractions?

Answer 5

Just like you would with integers.

Answer 6

9(9-8 (39/37))=2(39/37)+3 ??

Answer 7

\[|9-8 \cdot \frac{39}{37}|=\frac{2}{9} \cdot \frac{39}{37}+\frac{3}{9} \text{ Does this check out?}\]

Answer 8

OK. yes

Answer 9

Then you would do the same for x=84/70 (=6/5 if not mistaken)
\[|9-8 \cdot \frac{6}{5}|=\frac{2}{9} \cdot \frac{6}{5}+\frac{3}{9} \text{ Does this check out?}\]

Answer 10

Oh and your equation is fine to use. I just divided both sides by 9 before checking.

Answer 11

Yes, I caught that.

Answer 12

Do you recall the order of operations as far as mly, d, parenthesis, exponents ....??

Answer 13

wow - add, multiply is what that should say!

Answer 14

Do the operations inside the grouping symbols...
Like here we have the absolute value function which includes operations like multiplication and subtraction.
So in the absolute value part you would do the multiplication first and then the subtraction.
|9-8(39/37)|=|9-312/37|
Remember to subtract (or add) fractions we need to find a common denominator.

Answer 15

You simplify both sides using order of operations.
Then you see if both sides match.

Answer 16

312 came from where?

Answer 17

Multiplying 8 and 39/37.
I'm following the order of operations.

Answer 18

ok. I was onside o the equation trying to figure out where 312 came from.

Answer 19

Thank you.

Answer 20

You got it from there?

Answer 21

not sure.

Answer 22

seems like a lot of work. plugging the fractions in. I'm not good with fractions. trying.

Answer 23

multiplying them or adding them?

Answer 24

both :/

Answer 25

\[\frac{a}{b} \cdot \frac{c}{d}=\frac{a \cdot c}{b \cdot d} ; \frac{a}{b} \pm \frac{c}{d}=\frac{a \cdot d \pm c \cdot b}{b \cdot d}\]

Answer 26

so would you first multiply 2/9 and 39/37?

Answer 27

having the denominator 333?

Answer 28

78/333 +3/9=

Answer 29

For the other side of the equation?
Yes we have \[\frac{2}{9} \cdot \frac{39}{37} +\frac{1}{3}\]
mult first
\[\frac{36}{111}+\frac{1}{3}\]
Yes the denominator should be 333
\[\frac{36(3)+111(1)}{3(111)}\]

Answer 30

how did u get 111? 9(37) is 333

Answer 31

LCF?

Answer 32

I reduced the fraction during multiplication.

Answer 33

I got 78/333 + 1/3

Answer 34

2(39)/9(37)

Answer 35

+1/3 of course

Answer 36

\[\frac{2}{9}\cdot \frac{39}{37}=\frac{2}{3 \cdot 3} \cdot \frac{3 \cdot 13}{37}=\frac{2}{3 \cdot \cancel{3}} \cdot \frac{\cancel{3} \cdot 13}{37}=\frac{2 \cdot 13}{3 \cdot 37}\]

Answer 37

26/111
(and I made a type-o above)

Answer 38

This keyboard has sticky buttons :(

Answer 39

OK. 78/333 (my answer) if reduced is 26/111. We got the same answer. Now does that equal /9-312/37/??

Answer 40

Did you add the 1/3 yet?

Answer 41

oops. no.

Answer 42

so 26/111+1/3

Answer 43

\[\frac{2}{9} \cdot \frac{39}{37}+\frac{1}{3}=\frac{26}{111}+\frac{1}{3}=\frac{26(3)+1(111)}{111(3)}\]

Answer 44

189/333

Answer 45

so, now is = to/9-312/37/?

Answer 46

So how do you subtract 312/37 from 9?

Answer 47

I would make it a mixed number but I've been to use fractions. so, put a 1 under the 9??

Answer 48

9(37/37)-312/37
So we can have the same denominator