what is the number..?

Question

If 7 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 4 is added to the product. What is the number..?

 

Answer 1

The question gives us two equations. To find out what the number is, we have to set the two equations equal to each other. 

 

Lets make the number x. 

 

The first equation is described in the first half of the problem "If 7 is added to twice a number and this sum is multiplied by 6..." This tells us that we have to first multiply x by 2, which equals 2x, and add 7, which makes it 2x + 7. Then we need to multiply 2x+7 entirely by 6 (because we're multiplying the sum). Therefore, the first equation is 6(2x+7).

 

The second equation is described in the second half of the problem "the number is multiplied by -7 and 4 is added to the product." This means we need to multiply x by -7 and then add 4, which makes it -7x+4, which is the second equation.

 

We set the two equations equal to each other because the two equations, according to the problem, is the "same." Therefore, we get:

 

6(2x+7) = -7x+4

12x+42 = -7x+4

19x = -38

x = -2

 

Answer: The number is -2

 

 

Answer 2

6(2x+7)=-7x+4

12x+42=-7x+4

19x=-38

x=-2

Answer 3

Hi Tereza,

 

Let the number be x.

 

(2x+7)*6 = (-7)x+4

 

12x +42 = -7x+4

 

19x = -38

 

x=-2

 

Check: Lhs= (-4+7)*6=18

           Rhs= -7*(-2) +4=18

 

Answer 4

For this problem the easiest way to solve it is by writing an equation. If might seem really confusing but all we need to do is break it down into each action that is being taken.

 

Let x be the number we are trying to find. 

 

The descriptions tell us how to write the equation, we just have to break it all down:

 

• 7 is added to
• twice the number
• The sum of the above two is then multiplied by 6

 

That gives us the same answer as:

 

• multiplying the number by -7
• then adding 4

 

Now we just need to write this as an equation and solve for x

 

Starting with the first three bulletins:

 

(7 + 2x) * 6 =

 

Now the other two bulletins:

 

(-7)*x + 4 =

 

Now since these two equal the same number we can set them equal to each other and solve for x

 

6*(7 + 2x) = -7x + 4

 

42 + 12x = -7x + 4 

 

42 + 19x = 4

 

19x = -38

 

x = -2

 

To check this plug in the x value into the two separate sides of the equation:

 

42 + 12(-2) = -7(-2) + 4

 

42 + -24 = 14 + 4

 

18 = 18

 

Since we got that 18 = 18 we know that -2 is the correct answer.