Question

one positive integer is 4 less than another. the product of the two integers is 12. what are the integers?

Answer 1

Are you learning systems of equations?

Answer 2

Solving Problems With Quadratic Equations.. i need major help..

Answer 3

Ok. I'll help you.
We need to write an equation first.
You have 2 numbers, one is 4 less than the other.

Answer 4

Let x be the smaller of the two numbers.
What is the larger number in terms of x?
Remember that if the smaller number is 4 less than the larger number, then the larger number is 4 more than the smaller number.

Answer 5

i honestly do not know any of this.. im struggling so bad..

Answer 6

Ok.
Let's say a number is 6.
Then a number that is 4 more than 6 is 6 + 4 (which happens to be 10).

In our case, we don't know what the numbers are.
We are calling the smaller number x since it is unknown to us.
If the smaller number is x, then what is a number that is 4 more than x?
Do the same I did with 6 and 4 above.

Answer 7

What operation do you do to any number to end up with a number that is 4 more than the first number?

Answer 8

addition

Answer 9

are you there?..

Answer 10

Yes. It's addition.
If you add 4 to any number, you end up with a number that 4 more than the first number.
Here, we have chosen x to be the smaller number.
Then 4 more than x is the larger number.
4 more than x is x + 4

That means the two numbers are x and x + 4
Do you follow so far?

Answer 11

Are you still there?

Answer 12

yes

Answer 13

Do you understand that the numbers are x and x + 4?

Answer 14

yes i understand how you got them

Answer 15

Ok.
Now we follow the rest of the problem.
The problem states " the product of the two integers is 12."

Since the integers are x and x + 4, we multiply them and set the product equal to 12.

x(x + 4) = 12

Ok so far?

Answer 16

yes

Answer 17

are you there

Answer 18

My connection is messed up. I keep losing it.

Answer 19

Now you take the equation we have, multiply out the left side, subtract the number from the right side to the left, and you'll end up with a quadratic equation.

Answer 20

x(x + 4) = 12

We use the distributive property on the left side to get this:

\(x^2 + 4x = 12\)

Now we subtract 12 from both sides:

\(x^2 + 4x - 12 = 0\)

Now we need to solve the quadratic equation.
You can try factoring.

You need two numbers that add to 4 and multiply to -12.

Answer 21

2,-6??

Answer 22

oh wow really?

Answer 23

2 and -6 do multiply to -12, but they add to -4.
You need two numbers that multiply to -12 and add to 4, not -4.
You're close. If you just change the signs of your two numbers, you'll get them.