The sum of a number and 2 is 6 less than twice that number?

Question

please answer this question thanks

Answer 1

Let N=the number

 

Translate:

  "The sum of a number and 2 is 6 less than twice that number"     means

                       N        +     2  =  -6      +      2     *     N

 

Now, the easy math:

      N + 2 = -6 + 2N           (re-write)

           2  =  -6 + N          (subtract N from both sides)

           8  =  N                (add 6 to both sides)

 

Checking (very important):

   Is    8 + 2 = -6 + 2(8)   ?

          10    =   -6  + 16   ?

           10   =   10   ? yes

Answer 2

Kayla, math word problems can sometimes be "tricky" to answer. Look for words like "sum," "difference, " or other words that describe something dealing with mathematics.

 

Here we have the words "sum," "less," and "twice". Sum means to add, less means to subtract, and twice means to multiply.

 

Let the unknown number be n. Then the "sum of a number and 2" means to add our unknown number to 2.

 

The second part,  "6 less than twice the number" means to multiply the unknown number by 2 and then subtract 6 from the result.

 

We can set up an equation because the question tells us "the sum of a number and 2" is equal to "6 less than twice that number.

 

The equation is: 

 

n + 2 = 2n - 6

 

Combine like terms by subtracting n from both sides and adding 6 to both sides. I like to take it one step at a time.

 

Subtract n from both sides of the equation:

 

n - n + 2 = 2n - n - 6

 

Gives:

 

2 = n - 6

 

Add 6 to both sides of the equation:

 

2 + 6 = n - 6 + 6

 

Gives:

 

8 = n

 

The unknown number is 8. We can check our work by replacing the unknown number, n, in the original equation to see if the equation is true.

 

Original equation:

 

n + 2 = 2n - 6

 

8 + 2 = 2 * 8 - 6

 

10     = 16 - 6

 

10 = 10

 

Questions?