Chapter3: Graphs And Functions
Section3.4: Graph Linear Inequalities In Two Variables
Problem 3.82TI: Veronica works two part time jobs in order to earn enough money to meet her obligations of at least...
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Graph the solution set to the linear inequality on the number line
![### Graphing Linear Inequalities
**Question Details:**
- **Task:** Graph the solution set to the linear inequality
\[
-12x + 2 > 1
\]
on the number line below.
**Graph Details:**
- **Number Line:** The image displays a horizontal number line with arrows on both ends, indicating it extends infinitely in both directions.
**Solution Steps:**
1. **Solve the Inequality:**
- Start with the inequality: \(-12x + 2 > 1\).
- Subtract 2 from both sides: \(-12x > -1\).
- Divide by -12 and reverse the inequality sign (since dividing by a negative number reverses the inequality): \(x < \frac{1}{12}\).
2. **Graph the Solution:**
- On the number line, identify the point \(\frac{1}{12}\).
- Use an open circle at \(\frac{1}{12}\) to indicate that this point is not included in the solution (the inequality is less than, not less than or equal to).
- Shade the region to the left of \(\frac{1}{12}\) to represent all the values that are solutions to the inequality \(x < \frac{1}{12}\).
This activity helps in understanding how to graphically represent solutions to linear inequalities on a number line.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb228e09-4164-47f7-a050-f68b9f7ba773%2Fec3de42c-3f12-4955-ba17-4abe8984b03f%2Fme0cr1_processed.png&w=3840&q=75)
Transcribed Image Text:### Graphing Linear Inequalities
**Question Details:**
- **Task:** Graph the solution set to the linear inequality
\[
-12x + 2 > 1
\]
on the number line below.
**Graph Details:**
- **Number Line:** The image displays a horizontal number line with arrows on both ends, indicating it extends infinitely in both directions.
**Solution Steps:**
1. **Solve the Inequality:**
- Start with the inequality: \(-12x + 2 > 1\).
- Subtract 2 from both sides: \(-12x > -1\).
- Divide by -12 and reverse the inequality sign (since dividing by a negative number reverses the inequality): \(x < \frac{1}{12}\).
2. **Graph the Solution:**
- On the number line, identify the point \(\frac{1}{12}\).
- Use an open circle at \(\frac{1}{12}\) to indicate that this point is not included in the solution (the inequality is less than, not less than or equal to).
- Shade the region to the left of \(\frac{1}{12}\) to represent all the values that are solutions to the inequality \(x < \frac{1}{12}\).
This activity helps in understanding how to graphically represent solutions to linear inequalities on a number line.
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