Question

solve:
|4x-8|-3x=6x+2
and please write the solution set!!! thank you

Answer 1

get the absolute value part alone on one side
--> |4x-8| = 9x+2

then split it into 2 cases, positive and negative
--> 4x-8 = 9x+2
and
--> 4x-8 = -(9x+2)

Answer 2

and then please help me to solve it
i tried but with the absolute value i got them wrong

Answer 3

well we got rid of the abs value

can you solve the first case for x
4x-8 = 9x+2

Answer 4

this is what i did:

|4x-8|-3x=6x+2
4x-8=9x+2
-8=5x+2
-10=5x
-10/5=5x/5
x=-2

Answer 5

and when i plugged it in -2 works but the absolute value really kicks me off
because when you solve it then it turns into the same thing if there werent any absolute value

Answer 6

|4x-8|-3x=6x+2
|4(-2)-8|-3(-2)=6(-2)+2
|-8-8|-(-6)=-12+2
|-16|-(-6)=-10
|-16|+6=-10
|-10|=-10

Answer 7

but how can they be the same when there is an absolute value to the left side?

Answer 8

that is correct...so this means that x=-2 is an "extraneous solution" , it doesn't work
try the 2nd case

Answer 9

4x-8=-(9x+2)
4x-8=-9x-2
13x-8=-2
13x=6
13x/6=6/6
x=2.166

Answer 10

then that in turn creates a solution with a decimal so i dont think either works

Answer 11

almost...last step , divide by 13

13x = 6
x = 6/13

this should work when you plug it back in

Answer 12

0.4615285?

Answer 13

yes, if you want the decimal form :)

Answer 14

but will it work? because this is for alg 2.. and this is the only question that i am confused on

Answer 15

it will work
|4(6/13) -8| = 9(6/13) +2
|24/13 - 8| = 54/13 + 2
|-80/13| = 80/13
80/13 = 80/13

Answer 16

can you please explain how you did that?

Answer 17

i plugged in the solution x=6/13 into original equation
|4x-8| = 9x+2 , to check that it would work

for the fractions part
--> 24/13 - 8 = 24/13 - 104/13 = -80/13

--> 54/13 +2 = 54/13 + 26/13 = 80/13

Answer 18

so basically for the fractions you multiplied them?

Answer 19

yes...when multiplying fractions, top times top, bottom times bottom

Answer 20

okay thank you

Answer 21

welcome