Question

two negative integers are 8 units apart on the number line and have a product of 308. which equation could be used to determine x, the smaller negative integer? $x^2 + 8x - 308 = 0$ $x^2 - 8x + 308 = 0$ $x^2 + 8x + 308 = 0$ $x^2 - 8x - 308 = 0$

Explanation:

Step1: Define the larger integer

Let \( x \) be the smaller negative integer. Since the two negative integers are 8 units apart, the larger negative integer will be \( x + 8 \) (because on the number line, a larger negative integer is closer to zero, so if the smaller is \( x \), the larger is \( x + 8 \) as the distance between them is 8).

Step2: Set up the product equation

The product of the two integers is 308. So we have the equation:
\( x(x + 8) = 308 \)

Step3: Expand and rearrange the equation

Expanding the left - hand side: \( x^{2}+8x = 308 \)
Subtract 308 from both sides to get the quadratic equation in standard form: \( x^{2}+8x - 308=0 \)

Answer:

\( x^{2}+8x - 308 = 0 \) (The first option: \( x^{2}+8x - 308 = 0 \))