Math Problem Statement
Solve the compound inequality: -10 < 4x - 2 ≤ 10 and graph the solution on the number line.
Solution
To solve the compound inequality:
we can break it down into two parts:
Step 1: Solve the left inequality
Add 2 to both sides:
Then, divide by 4:
This gives us:
Step 2: Solve the right inequality
Add 2 to both sides:
Then, divide by 4:
Combine the Results
The solution for the compound inequality is:
Graphing the Solution
On the number line:
- Draw an open circle at (since does not include -2).
- Draw a closed circle at (since includes 3).
- Shade the region between and .
Would you like more details on each step, or have any questions about this solution?
Here are 5 related questions to expand your understanding:
- How would the solution change if the inequality were ?
- How do you solve a compound inequality with "or" instead of "and"?
- What are the steps to graph a strict inequality versus a non-strict inequality on a number line?
- How can we verify that our solution to a compound inequality is correct?
- How does dividing or multiplying by a negative number affect an inequality?
Tip: Always pay attention to the inequality signs, especially when dividing by negative numbers, as they reverse the direction of the inequality.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Compound Inequalities
Inequality Solving
Formulas
Solving compound inequalities by isolating the variable
Theorems
Inequality properties for addition, subtraction, multiplication, and division
Suitable Grade Level
Grades 7-10