Question

what is the sum of the solutions of

Answer 1

\[2\left| x-2\right|+3=4x+\]

Answer 2

5

Answer 3

so the right side is 4x+5

Answer 4

idk how to approach this problem. do i have to just have to solve them equal to each other?
Mutiple choice
a. -3
b. (-8/3)
c. (1/3)
d. (8/3)

Answer 5

@jim_thompson5910

Answer 6

ok just checking. The full equation is this?

\[\Large 2|x-2|+3=4x+5\]

Answer 7

yes

Answer 8

ok first subtract 3 from both sides

then after that divide both sides by 2

what do you get after those 2 steps are done?

Answer 9

\[\left| x-2 \right|=2x+1\]

Answer 10

good

Answer 11

now, we need to deal with that absolute value

Answer 12

we can break up the absolute value to form 2 equations

\[\left| x-2 \right|=2x+1 \Longrightarrow \begin{array}{c} x-2=2x+1\\ \text{OR}\\-(x-2)=2x+1\end{array} \]

so you need to solve x-2=2x+1 to get x = ??
and you need to solve -(x-2)=2x+1 to get x = ??

Answer 13

-3

Answer 14

`x = -3` is correct for the first equation. Solve `-(x-2)=2x+1` to get x = ??

Answer 15

1/3

Answer 16

good, so the two solutions are

x = -3 or x = 1/3

Answer 17

actually wait hold on

Answer 18

we need to check these possible solutions

Answer 19

the possible solutions are `x = -3 or x = 1/3`
plug each of them into the original equation. If you get a true equation, then it is definitely a solution. If not, then it is an extraneous solution.

Answer 20

isn't -3 extraneous

Answer 21

yep

Answer 22

ok, and i have a question you know the -(x-2) for the second equation we solved. can you put the negative one on the other side so -2x-1?

Answer 23

i mean -2x+1

Answer 24

well you can either have `-(x-2) = 2x+1` or `x-2 = -(2x+1)`

the negative will distribute through to get `x-2 = -2x-1`

Answer 25

ohh got u. thank you for the help!!:)

Answer 26

you're welcome