Question

Two negative integers are 8 units apart on the number line and have a product of 308. What equation could be used to determine x

Answer 1

Therefore the two negative integers are - 22, - 14.

Explanation:

Given that, two negative number are are 8 units apart.

Let x be a negative integer one of them.

Then the another integer be (x+8)

Given that the product of them is 308.

According to the problem,

`x(x+8)=308`

`\Rightarrow x^2+8x=308`

`\Rightarrow x^2+22x-14x-308=0`

`\Rightarrow x(x+22)-14(x+22)=0`

`\Rightarrow (x+22)(x-14)=0`

`\Rightarrow x=-22,14`

Since x is a negative integer.

∴x = - 22.

Then another integer is =( - 22+8) = -14

Therefore the two negative integers are - 22, - 14.