Algebra please explain?

7 - 5(1 - 2x) = 3(2x + 1)

Put the negative sign inside the brackets:

7 + 5(2x - 1) = 3(2x + 1)

Expand the brackets:

7 + 10x - 5 = 6x + 3

10x + 2 = 6x + 3

Subtract (6x + 2) from both sides of the equation:

4x = 1

Divide both sides by 4:

x = 1/4

For the second question, you are using the wrong notation. |x| is the absolute value of x, and you do not mean that, since an absolute value will always be positive (ie. |2x + 1| = -5 has no solution). Assuming you meant regular brackets:

2x + 1 = 5

Subtract 1 from both sides of the equation:

2x = 4

Divide both sides by 2:

x = 2

2x + 1 = -5

Subtract 1 from both sides of the equation:

2x = -6

Divide both sides by 2:

x = -3

7-5(1-2x)=3(2x+1)

7-5+10x=6x+3

4x=3-7+5=1

x=1/4

|2x+1|=5, 2x+1=5, 2x=4, x=2

|2x+1|=-5, 2x+1=-5, 2x=-5-1=-6, x=-3