Twice the difference of a number and 6 is equal to three times te sum of the number and 4. find the number.

-24

Step-by-step explanation:

Let the unknown number be x , therefore ; The difference between the number and 6 implies x - 6

Also , twice their difference implies 2 ( x - 6 )

The sum of the number and 4 implies : x + 4

three times their sum implies : 3 ( x + 4 )

Combining all together , we have

2 ( x - 6 ) = 3 ( x + 4 )

Expanding , we have

2x - 12 = 3x + 12

collecting the like terms , we have

2x - 3x = 12 + 12

-x = 24

multiply through by -, we have

x = -24

Check :

2 ( x - 6 ) will give

2 ( -24 - 6 )

= 2 (-30)

= -60

3 ( x+4) will give

3 ( -24 + 4 )

= 3 ( -20)

= -60

Therefore:

2( x- 6 ) = 3 ( x + 4 )

215.92 dollars is the answer