Question

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?

Answer 1

The number is -1.

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.

Answer 2

The number is -8

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