contestada

If 9 is added to twice a number and this sum is multiplied by 6​, the result is the same as if the number is multiplied by 7 and 14 is added to the product. What is the​ number?

Respuesta :

altavistard

Answer:

The number is -1.

Step-by-step explanation:

Let the number be represented by n.

Then "9 is added to twice a number and this sum is multiplied by 6" is represented by 2n + 9, and

" the number is multiplied by 7 and 14 is added to the product" is

7n + 14.

Then the complete equation is 2n + 9 = 7n + 14.

We must solve this for n.  To accomplish this, subtract 2n from both sides, obtaining 9 = 5n + 14.  Then subtract 14 from both sides, obtaining

-5 = 5n.  Then n must be -1.

jcherry99

Answer:

The number is -8

Step-by-step explanation:

Developing an equation

Read these phrases a little a time.

  • 9 is added to twice a number = 2x + 9
  • This sum is multiplied by 6 = 6* sum = 6 * (2x + 9) Note the brackets.
  • is the same thing as means =
  • the number multiplied by 7 = 7x
  • and 14 is added to the product 7x + 14
  • So what you have is equation: 6*(2x + 9) = 7x + 14

Solution

  • 6*(2x + 9) = 7x + 14               Remove the brackets on the left
  • 12x + 54 = 7x + 14                 Subtract 14 from both sides
  • 12x + 54 - 14 = 7x + 14 - 14    Collect terms
  • 12x + 40 = 7x                         Subtract 12x from both sides.
  • 12x - 12x + 40 = 7x - 12x        Combine
  • 40 = -5x                                 Divide by - 5
  • 40/-5 = x                                Do the division
  • - 8 = x

Otras preguntas