twice the sum of a number and 7 is equal to three times the difference of the number and 6. find the number

Step-by-step explanation: Let the number = x

"Twice the sum of a number and 6" is represented by:

2 (x+6)

Similarly, "Three times the difference of the number and 3" is represented by:

3 (x-3)

The given problem tells us that these are equal to each other:

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

Using the distributive property we get:

2x+12=3x-9

Subtract 2x from each side of the equation:

12=x-9

Add 9 to each side of the equation:

21=x - ->The number is 21.

To check, substitute 21 into 2 (x+6) = 3 (x-3) to determine if the statement is true:

2 (21+6) = 3 (21-3)

The order of operations tells us to complete the sum (and difference) in the parentheses first:

2 (27) = 3 (18) - -> 54=54

The statement is true.