Solve the following inequality and graph the solution: (x - 10) (x-8) 20 Choose test values and indicate whether the inequality is true or false in each region. Enter the test values from smallest to largest. Test Value Inequality 3 4 Select an answer 5 6 7 8 9 Select an answer 10 11 12 13 14 15 16 Clear All Draw: Select an answer Draw the solution above. Write the solution as a compound inequality ● O
Solve the following inequality and graph the solution: (x - 10) (x-8) 20 Choose test values and indicate whether the inequality is true or false in each region. Enter the test values from smallest to largest. Test Value Inequality 3 4 Select an answer 5 6 7 8 9 Select an answer 10 11 12 13 14 15 16 Clear All Draw: Select an answer Draw the solution above. Write the solution as a compound inequality ● O
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Solving Quadratic Inequalities**
### Inequality to Solve:
\[ (x - 10)(x - 8) \geq 0 \]
### Step-by-Step Solution and Graphing:
1. **Identify Key Points:**
Find the critical points by setting each factor equal to zero:
\[ x - 10 = 0 \implies x = 10 \]
\[ x - 8 = 0 \implies x = 8 \]
2. **Choose Test Values:**
Select test values in each of the regions created by the critical points and check the inequality:
- Region 1: \( x < 8 \)
- Region 2: \( 8 < x < 10 \)
- Region 3: \( x > 10 \)
Enter the test values from smallest to largest.
- **Region 1:** Test value \( \_\_\_\_ \)
- **Region 2:** Test value \( \_\_\_\_ \)
- **Region 3:** Test value \( \_\_\_\_ \)
3. **Evaluate the Inequality:**
Indicate whether the inequality is true or false for each test value.
**Test Value** | **Inequality**
-------------- | --------------
\_\_\_\_ | Select an answer
\_\_\_\_ | Select an answer
\_\_\_\_ | Select an answer
4. **Graph the Solution:**
Use the number line to plot the critical points and shade the regions where the inequality holds true.
- Enter the test values on the number line below the table.
- Draw the solution based on the true regions.
### Number Line
The number line below the table can be used to visualize the solution:
\[
3 \ 4 \ 5 \ 6 \ 7 \ 8 \ 9 \ 10 \ 11 \ 12 \ 13 \ 14 \ 15 \ 16
\]
Options to draw the solution:
- **➡:** Draw arrow to show the region.
- **⬤:** Solid dot to include the endpoint in the solution.
- **◯:** Open dot to exclude the endpoint from the solution.
### Final Steps:
1. **Draw the solution above.**
2. **Write the solution as a compound inequality.**
Compound Inequality](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70246055-557a-4851-8c33-1313c5079b88%2Fdd2f1a1d-6046-4820-a381-8e869ecbdeba%2Fszcars9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solving Quadratic Inequalities**
### Inequality to Solve:
\[ (x - 10)(x - 8) \geq 0 \]
### Step-by-Step Solution and Graphing:
1. **Identify Key Points:**
Find the critical points by setting each factor equal to zero:
\[ x - 10 = 0 \implies x = 10 \]
\[ x - 8 = 0 \implies x = 8 \]
2. **Choose Test Values:**
Select test values in each of the regions created by the critical points and check the inequality:
- Region 1: \( x < 8 \)
- Region 2: \( 8 < x < 10 \)
- Region 3: \( x > 10 \)
Enter the test values from smallest to largest.
- **Region 1:** Test value \( \_\_\_\_ \)
- **Region 2:** Test value \( \_\_\_\_ \)
- **Region 3:** Test value \( \_\_\_\_ \)
3. **Evaluate the Inequality:**
Indicate whether the inequality is true or false for each test value.
**Test Value** | **Inequality**
-------------- | --------------
\_\_\_\_ | Select an answer
\_\_\_\_ | Select an answer
\_\_\_\_ | Select an answer
4. **Graph the Solution:**
Use the number line to plot the critical points and shade the regions where the inequality holds true.
- Enter the test values on the number line below the table.
- Draw the solution based on the true regions.
### Number Line
The number line below the table can be used to visualize the solution:
\[
3 \ 4 \ 5 \ 6 \ 7 \ 8 \ 9 \ 10 \ 11 \ 12 \ 13 \ 14 \ 15 \ 16
\]
Options to draw the solution:
- **➡:** Draw arrow to show the region.
- **⬤:** Solid dot to include the endpoint in the solution.
- **◯:** Open dot to exclude the endpoint from the solution.
### Final Steps:
1. **Draw the solution above.**
2. **Write the solution as a compound inequality.**
Compound Inequality
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