Twice the sum of a number and 6 is equal to three times the difference of the number and 3. Find the number.

Question

Twice the sum of a number and 6 is equal to three times the difference of the number and 3. Find the number.

Answer 1

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.