Math Problem Statement
-7 < 2x - 9 ≤ 1. Solve the inequality.
Solution
Let's solve the given compound inequality step by step:
The inequality is:
Step 1: Solve the inequality in parts.
First part:
Add 9 to both sides:
Now, divide both sides by 2:
Second part:
Add 9 to both sides:
Now, divide both sides by 2:
Step 2: Combine the results.
From the two parts, we have:
Step 3: Write the solution in interval notation.
Since , the interval notation is:
Step 4: Graph the solution on the number line.
- The interval is from 1 to 5.
- At 1, use an open circle since .
- At 5, use a closed circle since .
Answer:
- The correct multiple-choice answer is: .
- The interval notation is: (1, 5].
Let me know if you'd like further clarification on any of these steps!
Here are some related questions you might want to explore:
- How do you solve compound inequalities with different inequality symbols?
- What is the difference between an open and closed interval on a number line?
- Can a compound inequality have no solution? In what cases?
- How do you graph inequalities on a number line with infinity in the solution?
- What is interval notation, and how does it differ from set-builder notation?
Tip: Always remember to handle each inequality in a compound inequality separately before combining the results!
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Math Problem Analysis
Mathematical Concepts
Compound Inequalities
Solving Linear Inequalities
Formulas
Inequality solving process: Isolate the variable
Linear inequality solving
Theorems
Basic inequality principles (addition and division)
Suitable Grade Level
Grades 8-10