Math Problem Statement
Solve the following inequality, and find the interval notation of the solution set: −3<2x+1≤5
Solution
Let's solve the inequality step by step:
We are given the inequality:
Step 1: Break it into two parts
We can break this compound inequality into two separate inequalities and solve each part:
Step 2: Solve the first inequality
Subtract 1 from both sides:
Now, divide both sides by 2:
Step 3: Solve the second inequality
Subtract 1 from both sides:
Now, divide both sides by 2:
Step 4: Combine the two results
We now have:
Step 5: Write the solution in interval notation
The solution set in interval notation is:
This means that is strictly greater than but less than or equal to .
Do you want more details or have any questions?
Here are 5 related questions:
- How do you solve inequalities involving absolute values?
- What is the difference between strict inequalities and non-strict inequalities?
- Can you explain how to solve inequalities involving quadratic expressions?
- How does interval notation differ from set notation?
- What happens when an inequality is multiplied or divided by a negative number?
Tip: When solving inequalities, remember that multiplying or dividing both sides by a negative number reverses the inequality sign.
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Math Problem Analysis
Mathematical Concepts
Algebra
Inequalities
Interval Notation
Formulas
Basic inequality manipulation (adding, subtracting, multiplying, and dividing)
Theorems
Properties of inequalities
Suitable Grade Level
Grades 7-9