Question

|3x+10|-|2x+1|=4
solve this please

Answer 1

one possibility
\[(-(3x+10))-(-(2x+1))\]

Answer 2

first possible solution was -13

second possiblity
\[((3x+10))-((2x+1))==4\]

=5

\[(-(3x+10))-((2x+1))==4\]
-3


\[((3x+10))-(-(2x+1))==4\]

-7/5

Answer 3

try -13, 5, -3, 7/5
only some will work

Answer 4

5 and -3 will not work

Answer 5

4 cases to look at:
-------------------------------------------------
3x+10>0 => |3x+10|=3x+10 (x>-10/3)
2x+1>0=> |2x+1|=2x+1 (x>-1/2)
()********
----|--------|--------
-10/3 -1/2

-------------------------------------------------
3x+10<0 => |3x+10|=-3x+10 (x<-10/3)
2x+1>0 => |2x+1|=2x+1 (x>-1/2)
****() ()**********
----|---------|---------
-10/3 -1/2
-------------------------------------------------
3x+10>0 => |3x+10|=3x+10 (x>-10/3)
2x+1<0 => |2x+1|=-(2x+1) (x<-1/2)
()***********()
---|----------|--------
-10/3 -1/2
-------------------------------------------------
3x+10<0 => |3x+10|=-(3x+10) (x<-10/3)
2x+1<0 => |2x+1|=-(2x+1) (x<-1/2)
***()
---|--------|-------
-10/3 -1/2
--------------------------------------------------
4 different cases:

Case 1:
(3x+10)-(2x+1)=4
3x+10-2x-1=4
x+9=4
x=-5
|3(-5)+10|-|2(-5)+1|=5-9=-4
also x=-5 is not in the range that we had above
-------------------------------------
Case 2:
-(3x+10)-(2x+1)=4
-3x-10-2x-1=4
-5x-11=4
-5x=15
x=-3
|3(-3)+10|-|2(-3)+1|= 1-5=-4 not 4
also not in range for case 2
-------------------------------------
Case 3:
(3x+10)--(2x+1)=4
5x+11=4
5x=-7
x=-7/5
|3(-7/5)+10|-|2(-7/5)+1|=4
YAY we found a solution!
-------------------------------------
Case 4:
-(3x+10)+(2x+1)=4
-3x-10+2x+1=4
-x-9=4
-x=13
x=-13
|3(-13)+10|-|2(-13)+1|=29-25= 4
YAY we have another solution
--------------------------------------
Sorry for delay. I was having an allergy attack.

Answer 6

Hope you are feeling all right