Question

Which of the following values are solutions to the inequality - 8 - 3x > 2?

I. – 2
II. – 12
III. 5

Answer 1

For the inequality -8 - 3x > 2, after isolating the variable x, we get x < -3.33. Checking the provided values, we find that only II. -12 satisfies the inequality. The answer to the question is II. -12.

Step-by-step explanation:

To solve the inequality -8 - 3x > 2, we must first isolate the variable x. We can do this by adding 8 to both sides of the inequality, resulting in -3x > 10. Next, we divide both sides by -3, remembering to reverse the inequality sign because we're dividing by a negative number, leading to x < -10/3 or approximately x < -3.33.

Now we can check which of the provided values satisfy the inequality:

• For I. -2: Substituting into the inequality, we have -8 - 3(-2) = -8 + 6 = -2, which is not greater than 2.
• For II. -12: Substituting this value, -8 - 3(-12) = -8 + 36 = 28, which is greater than 2. Therefore, -12 is a solution.
• For III. 5: Since 5 is greater than -3.33, it does not satisfy x < -3.33, making this value not a solution.

Hence, the only solution to the inequality -8 - 3x > 2 among the given values is II. -12.

Answer 2

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

X< -10/3

Interval Notation:

(-∞, - 10/3)

Hope this is right :)