A little algebra 1 help please... 10 points...

I really don't need the answer, I just need someone to explain this a little more to me...
14 + 2 l3x + 5l = 25 (Solving for X).
I came up with x = 1/3 but my teacher told me it was wrong....
Thank you.

14 + 2 l3x + 5l = 25

Absolute values give you the possibilities of two answers.
First assume (3x+5) >= 0
then |(3x + 5)| = 3x + 5
We work out the problem as
14 + 2(3x + 5) = 25
14 + 6x + 10 = 25
24 + 6x = 25
6x = 1
x = 1/6

Now we also have to consider the case where (3x + 5) < 0
Then |3x + 5| = -(3x + 5)
14 + 2 (-(3x + 5)) = 25
14 - 6x -10 = 25
-6x = 21
x = 21/-6 = -7/2

So there are two answers x = 1/6 or x = -7/2

Plug both back into the equation and you'll
14 + 2 l3x + 5l = 25
14 + 2 l3(1/6) + 5l = 25
14 + 2 l11/2l = 25
14 + 2(11/2) = 25
14 + 11 = 25
25 = 25 (True, answer checks)

14 + 2 l3x + 5l = 25
14 + 2 l3(-7/2) + 5l = 25
14 + 2 l-21/2 + 10/2l = 25
14 + 2|-11/2| = 25
14 + 2(11/2) = 25
14 + 11 = 25
25 = 25 (True, answer checks)

ok since that's clarified,
isolate x
2|3x+5| = 12
|3x+5|= 6 at this point, you must solve for 3x + 5 = 6 and 3x + 5 = -6
3x+5=6, 3x=1 x=1/3
3x+5=-6 3x=-11, x = -11/3

your teacher told you you were wrong because you were only half right. because it is an absolute value, that means there will be 2 different answers that satisfy the equation.

You are trying to work your way to the x. Start by subtracting 14 from both sides.

2|3x+5|=11

Then divide both sides by 2

|3x+5|=11/2

If those straight bars mean absolute value, then it is saying that 3x+5 could equal 11/2 or -11/2.

If it is 3x+5=11/2, then subtract 5 (same as 10/2)
3x=1/2

Divide by 3
x=1/6

OR 3x+5=-11/2
Same steps - subtract 5
3x= -21/2
divide by 3
x = -21/6 which reduces to -7/2

So the answers are 1/6 and -7/2

14 + 2 l3x + 5l = 25

2 l3x + 5l = 11

l3x + 5l = 11/2

3x + 5= 11/2 or -11/2

if it is 11/2, x= 1/6
-11/2, x= -7/2
so the answers are 1/6 & -7/2

x= 1/5