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

Answer: - 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)