Question

could someone show me how to find the absolute values of |2x+3|=|3x-4|

Answer 1

@jpjones do you know what does this imply |x|?

Answer 2

absolute value

Answer 3

good:)
we have
\[|2x+3|=|3x+4|\]
there are 2 cases
I) 2x+3>0
2) 2x+3<0

Answer 4

is it better to interprate |x| as +x or -x

Answer 5

yeah we'll get to that:)
if 2x+3\(\ge\)0
then
\[|2x+3|=2x+3\]
do you agree?

Answer 6

yes i agree

Answer 7

let's find the ranges, I did a mistake somewhere

Answer 8

if we solve
\[2x+3\ge0\]
we get
\[x\ge \frac{-3}{2}\]
so
for
\[x\ge -\frac{3}{2}=> |2x+3|=2x+3\]
and for
\[x< -\frac{3}{2}=> |2x+3|=-2x+3\]
Now would you do the same for 3x+4
find the ranges of x

Answer 9

i can tell you that the answer in the back of the book say's 1/5, and 7, so somewhere there is a mistake in your working, i must also explain that the question request all real values for x

Answer 10

@jpjones we haven't solved it yet

Answer 11

these are some points, which will help us to solve

Answer 12

ok

Answer 13

We'll start with a case let x be less than -3/2 then we'll get the equation as
3x+4<0 for x=-3/2
\[-(2x+3)=-(3x+4) \]
now we'll solve it to find x
if it comes out to be less than -3/2 then only it'll be an answer

Answer 14

do you get my point?

Answer 15

yes this statement is true but how do we solve from here

Answer 16

@jpjones Sorry there is an easy way, do you know quadratic equations?

Answer 17

yes

Answer 18

just square both sides then
\[(2x+3)^2=(3x-4)^2\]
what would you get now?

Answer 19

i'm a long way behind in my math and am trying to catch up, if you can't solve this let me know and i'll move on

Answer 20

No, we can solve this:)
would you simplify it?

Answer 21

Sorry the other way was long but it was also correct

Answer 22

i got 4x/9 =9x/16 cancel x, cancel 9 then left with 4/16 which is 1/4

Answer 23

after you square it, you'd get
\[4x^2+9+12x=9x^2+16-24x\]
can you solve it now?

Answer 24

no show me

Answer 25

do you know the quadratic formula?

Answer 26

@jpjones ??