Question
Which of the following values are solutions to the inequality \( -2>4 x-6 \) ? \[ \begin{array}{lll}\text { I. }-3 & \text { II. }-5 & \text { III. } 1\end{array} \]
Ask by Christensen Macdonald. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The values that satisfy the inequality are –3 and –5.
Solution
To determine which values satisfy the inequality \( -2 > 4x - 6 \), let's solve the inequality step by step:
1. **Start with the inequality:**
\[
-2 > 4x - 6
\]
2. **Add 6 to both sides to isolate the term with \( x \):**
\[
-2 + 6 > 4x
\]
\[
4 > 4x
\]
3. **Divide both sides by 4 to solve for \( x \):**
\[
1 > x \quad \text{or} \quad x < 1
\]
So, the solution to the inequality is all real numbers \( x \) such that \( x < 1 \).
Now, let's evaluate each given value:
- **I. \( x = -3 \):**
\[
-3 < 1 \quad \text{(True)}
\]
- **II. \( x = -5 \):**
\[
-5 < 1 \quad \text{(True)}
\]
- **III. \( x = 1 \):**
\[
1 < 1 \quad \text{(False)}
\]
**Conclusion:** Values I (\(-3\)) and II (\(-5\)) satisfy the inequality, but III (\(1\)) does not.
**Answer:** Only the values –3 and –5 satisfy the inequality.
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Extra Insights
To solve the inequality \( -2 > 4x - 6 \), we can start by isolating \( x \): 1. Add 6 to both sides: \[ -2 + 6 > 4x \] which simplifies to \[ 4 > 4x. \] 2. Now, divide both sides by 4: \[ 1 > x \] or \[ x < 1. \] Now we can check which of the provided values satisfy this condition: - I. For \( x = -3 \): Since \(-3 < 1\), it is a solution. - II. For \( x = -5 \): Since \(-5 < 1\), it is also a solution. - III. For \( x = 1 \): \( 1 < 1\) is false, so this is not a solution. Thus, the solutions to the inequality \( -2 > 4x - 6 \) are the values I. -3 and II. -5. So the solutions are: - **I. -3** - **II. -5**
