Which of the following values are solutions to the inequality 3, x, plus, 2, is greater than, minus, 3, question mark3x+2>−3?

Question

I., 0, II., minus, 8, III., minus, 9
I.0II.−8III.−9
Answer
Multiple Choice Answers
NoneNone
I onlyI only
II onlyII only
III onlyIII only
I and III and II
I and IIII and III
II and IIIII and III
I, II and IIII, II and III

Answer 1

To solve the inequality \( 3x + 2 > -3 \), we first isolate \( x \):

1. Subtract 2 from both sides: \[ 3x > -3 - 2 \] \[ 3x > -5 \]

2. Divide by 3: \[ x > -\frac{5}{3} \]

Now, let's evaluate the options against the inequality \( x > -\frac{5}{3} \) (which is approximately -1.67).

The given values are:

• I. \( 0 \)
• II. \( -8 \)
• III. \( -9 \)

Next, we check if each value satisfies the inequality:

1. Value I: \( 0 \) \[ 0 > -\frac{5}{3} \quad \text{(True)} \]

2. Value II: \( -8 \) \[ -8 > -\frac{5}{3} \quad \text{(False)} \]

3. Value III: \( -9 \) \[ -9 > -\frac{5}{3} \quad \text{(False)} \]

Based on the evaluations, only Value I (\( 0 \)) is a solution to the inequality.

Therefore, the correct answer is: I only.