Understanding One-Step Inequalities
One-step inequalities are a fundamental concept in mathematics, particularly in algebra and geometry. They involve solving an inequality by performing a single operation, such as addition, subtraction, multiplication, or division, on both sides of the inequality. In this article, we will explore the basics of one-step inequalities, provide examples, and offer worksheets to help you practice and reinforce your understanding.
What is an Inequality?
An inequality is a statement that compares two expressions using one of the following symbols:
- Less than (<)
- Greater than (>)
- Less than or equal to (≤)
- Greater than or equal to (≥)
For example, 2x + 3 < 5 is an inequality that compares the expression 2x + 3 to the value 5.
Solving One-Step Inequalities
To solve a one-step inequality, you need to isolate the variable (usually x) by performing a single operation on both sides of the inequality. The operation can be addition, subtraction, multiplication, or division.
Here are some examples:
- 2x < 6 (divide both sides by 2)
- x + 3 > 5 (subtract 3 from both sides)
- 4x ≥ 12 (divide both sides by 4)
- x - 2 ≤ 3 (add 2 to both sides)
When solving one-step inequalities, remember to:
- Add or subtract the same value to both sides
- Multiply or divide both sides by the same non-zero value
- Reverse the direction of the inequality symbol when multiplying or dividing by a negative value
📝 Note: When multiplying or dividing by a negative value, you must reverse the direction of the inequality symbol.
Worksheets for One-Step Inequalities
Here are some worksheets to help you practice solving one-step inequalities:
Worksheet 1: Solving One-Step Inequalities
| Inequality | Solution |
|---|---|
| 2x < 8 | x < 4 |
| x + 2 > 5 | x > 3 |
| 3x ≥ 9 | x ≥ 3 |
| x - 1 ≤ 2 | x ≤ 3 |
Worksheet 2: More One-Step Inequalities
| Inequality | Solution |
|---|---|
| 4x < 16 | x < 4 |
| x + 1 > 2 | x > 1 |
| 2x ≥ 6 | x ≥ 3 |
| x - 3 ≤ 1 | x ≤ 4 |
Worksheet 3: Mixed One-Step Inequalities
| Inequality | Solution |
|---|---|
| 2x + 1 < 5 | x < 2 |
| x - 2 > 1 | x > 3 |
| 3x ≥ 12 | x ≥ 4 |
| x + 2 ≤ 5 | x ≤ 3 |
Conclusion
Solving one-step inequalities is a fundamental skill in mathematics. By understanding the basics of inequalities and how to solve them, you can build a strong foundation for more advanced mathematical concepts. With practice and worksheets, you can become proficient in solving one-step inequalities and tackle more complex problems with confidence.
What is the difference between an equation and an inequality?
+
An equation is a statement that two expressions are equal, while an inequality is a statement that compares two expressions using less than, greater than, less than or equal to, or greater than or equal to.
How do I solve a one-step inequality?
+
To solve a one-step inequality, you need to isolate the variable by performing a single operation on both sides of the inequality. The operation can be addition, subtraction, multiplication, or division.
What happens when I multiply or divide both sides of an inequality by a negative value?
+
When you multiply or divide both sides of an inequality by a negative value, you must reverse the direction of the inequality symbol.
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