Question

Someone Help!!
Solve the equation. Check for extraneous solutions. Type your answers in the blanks. Show your work.
|4x+3| = 9 + 2x

x=_____ or ______

Answer 1

3

Answer 2

fan and medal and @ me for more help

Answer 3

@IQ250

Answer 4

yo

Answer 5

I need to understand the steps

Answer 6

\(\large\color{slate}{ |4x+3| = 9 + 2x }\)
this equation will give you two possible outcomes:

(outcome 1) \(\large\color{slate}{ 4x+3 = 9 + 2x }\)
(outcome 2) \(\large\color{slate}{ 4x+3 = -(9 + 2x) }\)

Answer 7

Now, solve each of the 'outcomes'

Answer 8

Lets start here:
Do you know what | x | means ?

Answer 9

For example,
| 4| is 4
and
|-4| is also 4

why? because it is "abolute value" (like distance) which can't be negative

Answer 10

If you have |x|=4
then x can be equal to 4 or -4 to make the statement true

Answer 11

I do not know what |x| means

Answer 12

okay so its |-4x-3| ?

Answer 13

And therefore if we have
`|4x+3| = 9 + 2x`
we are going to split it up like this:

4x+3 = 9 + 2x and 4x+3 = -(9 + 2x)

because the absolute value of 4x+3 can be equal to both 9 + 2x and -(9 + 2x)

Answer 14

As you are done reading, rate this to make sense please
from 1 (do not get it at all)
to 10 (perfectly understood)

Answer 15

(and after you rate it, if we can, I will proceed.)

Answer 16

|x| is a notation for "absolute value of x"

Answer 17

4

Answer 18

lets re-consider ` | 4 | ` (absolute value of 4) and ` | -4 | ` (absolute value of negative 4)

I am sure you have seen a number line before:


and you can certainly think :
| 4 | ` (absolute value of 4) as of a distance from 0 to 4 on a number line (which is equal to 4 [units])

| -4 | ` (absolute value of negative 4) as of a distance from 0 to -4 on a number line (which is equal to 4 [units])
(( distance is still 4, just that it is to the other direction)