X+6 ___ 2x+ 1

X + 3
___
2x - 1

x=  

11

​  

+1

x=1−  

11

​  

Step-by-step explanation:

(x+3)⋅(x−3)=2x+1

Consider (x+3)(x−3). Multiplication can be transformed into difference of squares using the rule: (a−b)(a+b)=a  

2

−b  

2

. Square 3.

x  

2

−9=2x+1

Subtract 2x from both sides.

x  

2

−9−2x=1

Subtract 1 from both sides.

x  

2

−9−2x−1=0

Subtract 1 from −9 to get −10.

x  

2

−10−2x=0

All equations of the form ax  

2

+bx+c=0 can be solved using the quadratic formula:  

2a

−b±  

b  

2

−4ac

​  

​  

. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

x  

2

−2x−10=0

This equation is in standard form: ax  

2

+bx+c=0. Substitute 1 for a, −2 for b, and −10 for c in the quadratic formula,  

2a

−b±  

b  

2

−4ac

​  

​  

.

x=  

2

−(−2)±  

(−2)  

2

−4(−10)

​  

​  

Square −2.

x=  

2

−(−2)±  

4−4(−10)

​  

​  

Multiply −4 times −10.

x=  

2

−(−2)±  

4+40

​  

​  

Add 4 to 40.

x=  

2

−(−2)±  

44

​  

​  

Take the square root of 44.

x=  

2

−(−2)±2  

11

​  

​  

The opposite of −2 is 2.

x=  

2

2±2  

11

​  

​  

Now solve the equation x=  

2

2±2  

11

​  

​  

 when ± is plus. Add 2 to 2  

11

​  

.

x=  

2

2  

11

​  

+2

​  

Divide 2+2  

11

​  

 by 2.

x=  

11

​  

+1

Now solve the equation x=  

2

2±2  

11

​  

​  

 when ± is minus. Subtract 2  

11

​  

 from 2.

x=  

2

2−2  

11

​  

​  

Divide 2−2  

11

​  

 by 2.

x=1−  

11

​  

The equation is now solved.

x=  

11

​  

+1

x=1−  

11

​  

water molecules will move from the side of higher water concentration to the side of lower concentration until both solutions are isotonic. at this point, equilibrium is reached. in an isotonic solution, the flow of water in and out of the cell is happening at the same rate.

hope this < 3

people went from manufacturing one object at a time by hand to manufacturing many objects in factories