We are given that 13*|2x+1|=26

13*|2x+1|=26

divide both sides by 13

=> |2x +1| = 2

Now |2x +1| = 2

=> 2x +1 = 2 and 2x +1 = -2

=> 2x = 1 and 2x = -3

=> x = 1/2 and x = -3/2

**Therefore x is equal to 1/2 and -3/2.**

To find x if 13*|2x+1|=26.

We divide both sides by 13:

|2x+1| = 26/13 = 2.

|2x+1| = 2.

If 2x+1 > 0, then |2x+1| = 2 implies 2x+2 = 2.

=> 2x+1-1 = 2-1.

=> 2x= 1.

=> 2x/2 = 1/2 .

x = 1/2.

So x= 0.5.

If (2x+1) < 0, |2x+1| = 2 => 2x+1= -2.

=> 2x+1-1 = -2-1.

=> 2x => -3.

=> 2x/2 = -3/2 = -1.5.

So x= -1.5.

Therefore x = 0.5, or x= -1.5.

We'll solve the equation, expressing first the modulus.

Case 1:

l 2x + 1 l = 2x + 1 for 2x + 1 >= 0

2x >= -1

x >= -1/2

Now, we'll solve the equation:

13(2x + 1) = 26

We'll divide by 13:

2x + 1 = 2

2x = 2-1

**x = 1/2**

Since x =1/2 is in the interval of admissible values,[-1/2, +infinite], we'll accept it.

Case 2:

l 2x + 1l = -2x - 1 for 2x + 1 < 0

2x < -1

x < -1/2

Now, we'll solve the equation:

13(-2x - 1) = 26

-2x - 1 = 2

-2x = 3

**x = -3/2**

Since x = -3/2 is in the interval of admissible values, (-infinite, -1/2), we'll accept it.