Solving One Step Inequalities Made Easy for You

Solving One Step Inequalities: A Comprehensive Guide

Solving one step inequalities is a fundamental concept in mathematics, particularly in algebra. It’s essential to understand how to solve these types of inequalities to progress to more complex math problems. In this article, we’ll break down the process of solving one step inequalities into simple, easy-to-follow steps.

What are One Step Inequalities?

One step inequalities are inequalities that can be solved in one step, either by addition, subtraction, multiplication, or division. These inequalities typically involve a single variable and a constant term. The goal is to isolate the variable on one side of the inequality sign.

Types of One Step Inequalities

There are four types of one step inequalities, each with a different operation:

• Addition inequalities: ax + b > c
• Subtraction inequalities: ax - b > c
• Multiplication inequalities: ax * b > c
• Division inequalities: ax / b > c

Solving One Step Inequalities

To solve one step inequalities, follow these steps:

1. Add or subtract the same value to both sides: If the inequality involves addition or subtraction, add or subtract the same value to both sides of the inequality to isolate the variable.
2. Multiply or divide both sides by the same value: If the inequality involves multiplication or division, multiply or divide both sides of the inequality by the same value to isolate the variable.
3. Simplify the inequality: Combine like terms and simplify the inequality.

Examples:

• 2x + 5 > 11 (addition inequality)
  • Subtract 5 from both sides: 2x > 6
  • Divide both sides by 2: x > 3
• x - 3 < 7 (subtraction inequality)
  • Add 3 to both sides: x < 10
• 4x > 24 (multiplication inequality)
  • Divide both sides by 4: x > 6
• x / 2 < 9 (division inequality)
  • Multiply both sides by 2: x < 18

Important Rules to Remember

When solving one step inequalities, remember the following rules:

• When multiplying or dividing both sides of an inequality by a negative number, flip the direction of the inequality sign.
• When adding or subtracting a negative number, flip the sign of the number.

📝 Note: These rules are crucial to ensure that the inequality sign is in the correct direction.

Common Mistakes to Avoid

When solving one step inequalities, avoid the following common mistakes:

• Flipping the inequality sign incorrectly: Double-check that you’re flipping the inequality sign in the correct direction when multiplying or dividing by a negative number.
• Forgetting to simplify: Simplify the inequality by combining like terms to ensure the solution is accurate.

Practice Problems

Practice solving one step inequalities with the following problems:

• 3x + 2 > 14
• x - 4 < 9
• 2x > 16
• x / 3 < 6

Solving One Step Inequalities with Tables

Sometimes, it’s helpful to use a table to visualize the solution to a one step inequality. Here’s an example:

In this example, we’re solving the inequality 2x + 3 > 7. We create a table with values of x and calculate the corresponding values of 2x + 3. We then determine which values of x satisfy the inequality.

Solving one step inequalities is a fundamental concept in mathematics. By following these simple steps and remembering the important rules, you’ll become proficient in solving one step inequalities in no time.

In conclusion, solving one step inequalities requires attention to detail and a solid understanding of mathematical operations. By practicing regularly and using tables to visualize the solution, you’ll become more confident in your ability to solve these types of inequalities.