solve for x. |3x-2| = |2x+5|+1
okay so for these one it be |3x-2| = |2x+5| because 1 times in with |2x+5| or it be (-2x-5)
i think that be wrong the real answer have to be -4/5 and 8 i just not know how to get thats.
if 3x-2 > 0 then |3x-2| = 3x-2
if 2x+5 > 0 then |2x+5| = 2x+5
in this case,
3x-2 = 2x+5 + 1
x = 8
since 8 satisfies the conditions, it is a solution
if 3x-2 < 0 then |3x-2| = -(3x-2)
if 2x+5 > 0 then |2x+5| = 2x+5
in this case,
-(3x-2) = 2x+5 + 1
x = -4/5
since -4/5 satisfies the conditions, it is a solution
If you work through the other two choices, you will either find no more solutions, or duplicates of these.
To solve the equation |3x-2| = |2x+5|+1, we need to consider two cases:
Case 1: (3x-2) = (2x+5)+1
In this case, we can solve for x:
3x - 2 = 2x + 6
Subtract 2x from both sides:
x - 2 = 6
Add 2 to both sides:
x = 8
Case 2: (3x-2) = -(2x+5)+1
In this case, we solve for x similarly:
3x - 2 = -2x - 5 + 1
Add 2x to both sides:
5x - 2 = -4
Add 2 to both sides:
5x = -2
Divide by 5 on both sides:
x = -2/5
So, the two solutions to the equation are x = 8 and x = -2/5.