Question

Find the sum of the solutions:
5│x│ - 3 = │3x + 7│

Answer 1

\[5\left| x \right|-3 = \left| 3x+7 \right|\]

Answer 2

How would I go about this?

Answer 3

Are things in absolute value "like terms?"

Answer 4

?

Answer 5

Let's consider some cases:
-------------------------------------------
\[\text{ CASE 1:} x>0 ; x>\frac{-7}{3}\]
|x|=x ; |3x+7|=3x+7
5(x)-3=3x+7
solve this for x
and then check it
--------------------------------------------
\[\text{ CASE 2:} x>0; x<\frac{-7}{3}\]
|x|=x; |3x+7|=-(3x+7)
5(x)-3=-(3x+7)
solve this for x
and check it
--------------------------------------------
\[\text{ CASE 3: } x<0; x>\frac{-7}{3}\]
|x|=-x ; |3x+7|=3x+7
5(-x)-3=3x+7
solve this for x
and check it
--------------------------------------------
\[\text{ CASE 4: } x<0 ; x<\frac{-7}{3}\]
|x|=-x; |3x+7|=-(3x+7)
5(-x)-3=-(3x+7)
solve this for x
and check it

Answer 6

Is that how you have to do it?

Answer 7

and i dont understand the "Cases"

Answer 8

i'm looking at when |x|=x or when it is |x|=-x
and something for |3x+7|

Answer 9

what do you mean by something for │3x + 7│

Answer 10

same thing*

Answer 11

Can you try to explain it a different way. I'm sorry

Answer 12

|3x+7|=3x+7 when 3x+7>0
|3x+7|=-(3x+7) when 3x+7<0
|x|=x when x>0
|x|=-x when x<0

Answer 13

i looked at all possible combinations of these

Answer 14

that is how i got my 4 cases

Answer 15

Okay. Thanks. It's more clear now.

Answer 16

i actually wrote this above when i did the 4 cases

Answer 17

3x+7>0 => x>-7/3
after solve for x
3x+7<0 => x<-7/3
after solving for x

Answer 18

i'm glad you understand though :)