Which graph represents the solution to 3x – 2 > 1? A + -5 -4 -3 -2 -1 0 1 3 4 5 B + + + -5 -4 -3 -2 -1 0 1 3 4 5 © + + -5 -4 -3 -2 -1 0 1 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5

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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### Which graph represents the solution to \(3x - 2 > 1\)?

To solve the inequality \(3x - 2 > 1\), we first add 2 to both sides:

\[3x > 3\]

Next, divide both sides by 3:

\[x > 1\]

Now, let's examine the graphs:

**Graph A:**

- A number line from -5 to 5.
- An open circle at 1.
- A line with an arrow extending to the right from 1, representing all numbers greater than 1.

**Graph B:**

- A number line from -5 to 5.
- An open circle at 1.
- A line with an arrow extending to the left from 1, representing all numbers less than 1.

**Graph C:**

- A number line from -5 to 5.
- An open circle at 1.
- A line with an arrow extending to the right from 1, representing all numbers greater than 1.

**Graph D:**

- A number line from -5 to 5.
- A filled circle at 1.
- A line with an arrow extending to the left from 1, representing all numbers less than or equal to 1.

The correct solution is **Graph A** because it shows an open circle at 1 with a line extending to the right, representing all numbers greater than 1.
Transcribed Image Text:### Which graph represents the solution to \(3x - 2 > 1\)? To solve the inequality \(3x - 2 > 1\), we first add 2 to both sides: \[3x > 3\] Next, divide both sides by 3: \[x > 1\] Now, let's examine the graphs: **Graph A:** - A number line from -5 to 5. - An open circle at 1. - A line with an arrow extending to the right from 1, representing all numbers greater than 1. **Graph B:** - A number line from -5 to 5. - An open circle at 1. - A line with an arrow extending to the left from 1, representing all numbers less than 1. **Graph C:** - A number line from -5 to 5. - An open circle at 1. - A line with an arrow extending to the right from 1, representing all numbers greater than 1. **Graph D:** - A number line from -5 to 5. - A filled circle at 1. - A line with an arrow extending to the left from 1, representing all numbers less than or equal to 1. The correct solution is **Graph A** because it shows an open circle at 1 with a line extending to the right, representing all numbers greater than 1.
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