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.
