Solve the inequality. Write the solution set in interval notation. - 4x + 4s 12 The solution set is (Use integers or decimals for any numbers in the expression.)
Solve the inequality. Write the solution set in interval notation. - 4x + 4s 12 The solution set is (Use integers or decimals for any numbers in the expression.)
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 Inequalities
To solve the given inequality, follow these steps:
1. **Understand the Inequality**:
- The inequality given is: \(-4x + 4 \leq 12\)
2. **Isolate the Variable (x)**:
- First, subtract 4 from both sides to isolate the term with \(x\):
\[
-4x \leq 12 - 4
\]
- This simplifies to:
\[
-4x \leq 8
\]
- Next, divide both sides by \(-4\). Remember to reverse the inequality sign when you divide by a negative number:
\[
x \geq -2
\]
3. **Write the Solution Set in Interval Notation**:
- The solution \(x \geq -2\) can be written in interval notation as:
\[
[-2, \infty)
\]
### Summary:
- **Problem**: Solve the inequality \(-4x + 4 \leq 12\).
- **Solution**: The solution set in interval notation is \([-2, \infty)\).
**Note**: Use integers or decimals for any numbers in the expression if writing or typing it out.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7bd99ef-7092-4177-9c19-951c55d49391%2Fbb018126-d1df-4af6-bf36-b5c4bef4ce20%2F1z3ne2q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving Inequalities
To solve the given inequality, follow these steps:
1. **Understand the Inequality**:
- The inequality given is: \(-4x + 4 \leq 12\)
2. **Isolate the Variable (x)**:
- First, subtract 4 from both sides to isolate the term with \(x\):
\[
-4x \leq 12 - 4
\]
- This simplifies to:
\[
-4x \leq 8
\]
- Next, divide both sides by \(-4\). Remember to reverse the inequality sign when you divide by a negative number:
\[
x \geq -2
\]
3. **Write the Solution Set in Interval Notation**:
- The solution \(x \geq -2\) can be written in interval notation as:
\[
[-2, \infty)
\]
### Summary:
- **Problem**: Solve the inequality \(-4x + 4 \leq 12\).
- **Solution**: The solution set in interval notation is \([-2, \infty)\).
**Note**: Use integers or decimals for any numbers in the expression if writing or typing it out.
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