Two negative integers are 5 units apart on the number line, and their product is 126. what is the sum of the two integers?
a. –23
b. –5
c. 9
d. 14
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Step-by-step explanation:

| x - y | = 5

x * y = 126

x = -9; y = -14

x + y = -23

I'm not sure this may help you since I don't know how well you are at mental math so I just used guess and check by checking which pair of numbers would work.

Since the numbers are 5 apart, and they're both negative, I check which pair is equal to 126.

-6 * -11 = 66

...

-9 * -14 = 126

Remember to start from a reasonable area.  

Also, I just realized that you can use the process of elimination for this question last minute.  Since both numbers are negative, they add up to a negative number so you can cross off C and D.  You can cross of B since the only way to end up with a sum of -5 is if you end up having 0 and -5, and 0 * (-5) = 0.

Please mark for Brainliest

For more information, please comment below and I'll respond asap!!

A

- 23

Step-by-step explanation:

Two negative numbers differ by 5

Let the smaller one be x

Let the larger one be y

y - x = 5                    this will give you a plus. Let us suppose the numbers are -20 and -25.  - 25 is smaller than - 20. Which would you rather be, 20 dollars in debt or 25 dollars in debt?

So using -20 - - 25 = 5

y = x + 5                   Obtained by adding x to both sides.

xy = 126

You can eliminate C and D. Both are positive. That's not what the question says.

xy = 126                          Put  y = x + 5 in for y.

x(x + 5) = 126                  Remove the brackets

x^2 + 5x = 126                Subtract 126 from both sides.

x^2 + 5x - 126 = 0           Factor

(x + 14)(x - 9) = 0

You cannot use x - 9 = 0 because 9 is not a negative number.

x + 14 = 0

x = - 14

y = x + 5

y = -14 + 5

y = - 9

The sum of the two numbers is

- 14 + -9 = - 23