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.

{3 + i, 3 - i, 3, -1}

step-by-step explanation: