QQuestionMathematics
QuestionMathematics
Which compound inequality is represented by the graph?
\begin{aligned}
& - 2<x \leq 4 \\
& - 2 \leq x<4 \\
& x<- 2 \text { or } x \geq 4 \\
& x \leq- 2 \text { or } x>4
\end{aligned}
12 months agoReport content
Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
Step 1:Let's solve this step by step by carefully analyzing the graph and comparing it to the given inequality options.
Step 2:: Examine the graph characteristics
- The graph shows a number line with: * A closed circle (filled dot) at - 2 * An open circle (hollow dot) at 4 * The shaded region is between - 2 and 4
Step 3:: Identify the key graph features
- Closed circle at - 2 means - 2 is included in the interval - Open circle at 4 means 4 is NOT included in the interval - Shaded region represents the solution set
Step 4:: Compare graph features to given inequalities
- We need an inequality that: * Includes - 2 (closed circle) * Excludes 4 (open circle) * Represents the shaded region between these points
Step 5:: Evaluate each option
* Excludes 4 (strict $$<$$)
* Matches the graph EXACTLY
Final Answer
The correct compound inequality is - 2 < x \leq 4.
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students