Solve the equation and inequalities. Write the solution sets in interval notation if possible. (a) (2x-7)(x-8)=0 (b) (2x-7)(x-8) <0 (c) (2x-7)(x-8) ≤0 (d) (2x-7)(x-8)>0 (e) (2x-7)(x-8) 20
Solve the equation and inequalities. Write the solution sets in interval notation if possible. (a) (2x-7)(x-8)=0 (b) (2x-7)(x-8) <0 (c) (2x-7)(x-8) ≤0 (d) (2x-7)(x-8)>0 (e) (2x-7)(x-8) 20
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.7: Solving Systems Of Linear And Quadratic Equations
Problem 5CYU
Related questions
Question
![### Solving Equations and Inequalities
**Instructions:** Solve the equations and inequalities given below. Write the solution sets in interval notation if possible.
#### Problems:
(a) \((2x - 7)(x - 8) = 0\)
(b) \((2x - 7)(x - 8) < 0\)
(c) \((2x - 7)(x - 8) \leq 0\)
(d) \((2x - 7)(x - 8) > 0\)
(e) \((2x - 7)(x - 8) \geq 0\)
---
**Part 1 of 5**
**(a) \((2x - 7)(x - 8) = 0\)**
The solution set is:
- There is a graphical user interface in the image with various symbols. Users need to select the correct symbols to represent the solution set correctly.
In this case, the solutions to the equation \((2x - 7)(x - 8) = 0\) would be:
- \(2x - 7 = 0\) implies \(x = \frac{7}{2} = 3.5\)
- \(x - 8 = 0\) implies \(x = 8\)
Therefore, the solution set is: \(\left\{ 3.5, 8 \right\}\)
**To Input the Solution Set:**
- Open the solution input area.
- Select the bracketing symbols (curly braces) representing a set.
- Input the values \(3.5\) and \(8\) within these brackets.
For visual understanding:
- The interface displays clickable options for various interval notations and their combinations. Ensure to choose correctly to match the solution format expected.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4830af55-84e9-44a3-a1a9-c9fad267ce9b%2Fc873cd69-de12-4198-aacd-73033ccd1676%2F6r6cobq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving Equations and Inequalities
**Instructions:** Solve the equations and inequalities given below. Write the solution sets in interval notation if possible.
#### Problems:
(a) \((2x - 7)(x - 8) = 0\)
(b) \((2x - 7)(x - 8) < 0\)
(c) \((2x - 7)(x - 8) \leq 0\)
(d) \((2x - 7)(x - 8) > 0\)
(e) \((2x - 7)(x - 8) \geq 0\)
---
**Part 1 of 5**
**(a) \((2x - 7)(x - 8) = 0\)**
The solution set is:
- There is a graphical user interface in the image with various symbols. Users need to select the correct symbols to represent the solution set correctly.
In this case, the solutions to the equation \((2x - 7)(x - 8) = 0\) would be:
- \(2x - 7 = 0\) implies \(x = \frac{7}{2} = 3.5\)
- \(x - 8 = 0\) implies \(x = 8\)
Therefore, the solution set is: \(\left\{ 3.5, 8 \right\}\)
**To Input the Solution Set:**
- Open the solution input area.
- Select the bracketing symbols (curly braces) representing a set.
- Input the values \(3.5\) and \(8\) within these brackets.
For visual understanding:
- The interface displays clickable options for various interval notations and their combinations. Ensure to choose correctly to match the solution format expected.
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