Graph the solution set to the linear inequality -12x + 2 > 1 on the number line below.

Intermediate Algebra
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ISBN:9780998625720
Author:Lynn Marecek
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Chapter3: Graphs And Functions
Section3.4: Graph Linear Inequalities In Two Variables
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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.
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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