Question

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

Answer 1

To solve the problem, define the unknown number as 'x' and set up an equation. Simplify the equation by expanding the brackets and combining like terms. Solve for 'x' by isolating it on one side of the equation. The solution is x = 32.

Step-by-step explanation:

To solve this problem, let's define the unknown number as 'x'. According to the problem, twice the sum of the number and 7 is equal to three times the difference of the number and 6.

Mathematically, this can be written as 2(x + 7) = 3(x - 6).

Now, let's solve for 'x':

1. Expand the brackets: 2x + 14 = 3x - 18.
2. Subtract 2x from both sides: 14 = x - 18.
3. Add 18 to both sides: 32 = x.

Therefore, the number is 32.

Answer 2

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.