Solving One-Step Inequalities
Welcome to the lesson on solving one-step inequalities! This lesson is designed for Grade 9 Algebra I students and will cover the basics of solving simple inequalities. We will provide examples, exercises, and solutions to help you master this topic.
Outline
- Introduction to One-Step Inequalities
- Examples
- Exercises with Solutions
- Homework
- Revision
- YouTube Video
Introduction to One-Step Inequalities
One-step inequalities are inequalities that can be solved in a single step. These inequalities involve basic operations such as addition, subtraction, multiplication, or division.
Examples
Example 1: Solving \( x + 5 < 12 \)
To solve this inequality, subtract 5 from both sides:
\( x + 5 - 5 < 12 - 5 \)
\( x < 7 \)
Example 2: Solving \( 3x > 9 \)
To solve this inequality, divide both sides by 3:
\( \frac{3x}{3} > \frac{9}{3} \)
\( x > 3 \)
Example 3: Solving \( \frac{x}{4} \leq 2 \)
To solve this inequality, multiply both sides by 4:
\( 4 \times \frac{x}{4} \leq 4 \times 2 \)
\( x \leq 8 \)
Example 4: Solving \( x - 7 \geq 3 \)
To solve this inequality, add 7 to both sides:
\( x - 7 + 7 \geq 3 + 7 \)
\( x \geq 10 \)
Example 5: Solving \( -2x < 6 \)
To solve this inequality, divide both sides by -2 and remember to reverse the inequality sign:
\( \frac{-2x}{-2} > \frac{6}{-2} \)
\( x > -3 \)
Example 6: Solving \( 5 \geq \frac{x}{3} \)
To solve this inequality, multiply both sides by 3:
\( 5 \times 3 \geq \frac{x}{3} \times 3 \)
\( 15 \geq x \)
Or \( x \leq 15 \)
Exercises with Solutions
Exercise 1
Solve \( x + 8 \leq 15 \)
Subtract 8 from both sides:
\( x + 8 - 8 \leq 15 - 8 \)
\( x \leq 7 \)
Exercise 2
Solve \( 4x > 20 \)
Divide both sides by 4:
\( \frac{4x}{4} > \frac{20}{4} \)
\( x > 5 \)
Exercise 3
Solve \( \frac{x}{5} \geq 3 \)
Multiply both sides by 5:
\( 5 \times \frac{x}{5} \geq 3 \times 5 \)
\( x \geq 15 \)
Exercise 4
Solve \( x - 4 > 6 \)
Add 4 to both sides:
\( x - 4 + 4 > 6 + 4 \)
\( x > 10 \)
Exercise 5
Solve \( -3x \leq 9 \)
Divide both sides by -3 and reverse the inequality sign:
\( \frac{-3x}{-3} \geq \frac{9}{-3} \)
\( x \geq -3 \)
Exercise 6
Solve \( 7 \geq \frac{x}{2} \)
Multiply both sides by 2:
\( 7 \times 2 \geq \frac{x}{2} \times 2 \)
\( 14 \geq x \)
Or \( x \leq 14 \)
Homework
Complete the following problems for practice:
- Solve \( x + 9 < 18 \)
- Solve \( 6x \geq 24 \)
- Solve \( \frac{x}{4} \leq 5 \)
- Solve \( x - 3 > 8 \)
- Solve \( -5x < 15 \)
- Solve \( 10 \geq \frac{x}{3} \)
Revision
In this lesson, we learned how to solve one-step inequalities by performing basic operations such as addition, subtraction, multiplication, and division. We discussed how to handle inequalities involving different operations and how to reverse the inequality sign when multiplying or dividing by a negative number.
YouTube Video
Watch this video for a visual explanation of solving one-step inequalities.
Contact Us
If you have any questions or need further assistance, please contact us for tutoring online or text our numbers to book a tutor. Follow us on Facebook and YouTube for more updates and educational content.
0 Comments