Question

Which of the following values are solutions to the inequality 7 < -2 – 3x?

I. 1
II. 3
III. - 3
None

I only
II only
III only
I and II
I and III
II and III

Answer 1

The solution to the inequality 7 < -2 – 3x is 'II only', which corresponds to the value x = 3, as it is the only provided value greater than -3.

Step-by-step explanation:

The inequality in question is 7 < -2 – 3x. To determine which values are solutions to this inequality, we solve for x:

1. Add 2 to both sides of the inequality: 7 + 2 < -3x, which simplifies to 9 < -3x.
2. Divide both sides by -3, remembering to reverse the inequality because we are dividing by a negative number: -3 < x.
3. This inequality means that x must be greater than -3.

Now we test the given options:

• I. 1 is not greater than -3, so it is not a solution.
• II. 3 is greater than -3, so it is a solution.
• III. -3 is not greater than -3, so it is not a solution.

Therefore, the correct answer is II only.