I am not sure 2|2x-3|-5=25 is x=6, x=9?

2|2x - 3| - 5 = 25

To solve this, we first need to get the absolute value by itself. So in doing that, we get:

2|2x - 3| = 30
|2x - 3| = 15

Now solving this, removing the absolute value places a ± on the other side. Simple example:

|x| = 2
x = ±2

Since both -2 and +2 are solutions.

so doing that, we get:

2x - 3 = ±15

now solve for our two x's:

2x = 3 ± 15
2x = -12 and 2x = 18
x = -6 and x = 9

So to answer your question: is the answer x = 6 and x = 9? no. It is not.

The answer is:

x = -6 and x = 9

Testing the answers, we get:

2|2x - 3| - 5 = 25
2|2(-6) - 3| - 5 = 25 and 2|2(9) - 3| - 5 = 25
2|-12 - 3| - 5 = 25 and 2|18 - 3| - 5 = 25
2|-15| - 5 = 25 and 2|15| - 5 = 25
2(15) - 5 = 25 and 2(15) - 5 = 25

And now both equations are the same, so only simplifying it once:

30 - 5 = 25
25 = 25
TRUE

So both x = -6 and x = 9 are answers.

I 2x - 3 I = 15
2x - 3 = - 15 or 2x - 3 = 15
x = - 6 , x = 9

Not sure iether