Understanding One-Step Equations
One-step equations are simple algebraic equations that can be solved in just one step. These equations typically involve adding, subtracting, multiplying, or dividing both sides of the equation by a single value to isolate the variable. In this blog post, we will explore one-step equations, their importance, and provide a worksheet to help students practice solving these equations.
What are One-Step Equations?
One-step equations are algebraic equations that require only one operation to solve. These equations usually have one variable, and the goal is to isolate that variable on one side of the equation. One-step equations can be in the form of addition, subtraction, multiplication, or division.
Examples of One-Step Equations:
- 2x = 6 (multiplication)
- x + 3 = 7 (addition)
- x - 2 = 9 (subtraction)
- x/4 = 9 (division)
Why are One-Step Equations Important?
One-step equations are essential in mathematics, as they help build the foundation for more complex algebraic equations. Solving one-step equations develops problem-solving skills, critical thinking, and logical reasoning. These equations are also used in real-world applications, such as science, engineering, economics, and finance.
Solving One-Step Equations
To solve one-step equations, follow these steps:
- Read the equation carefully: Identify the variable, constants, and the operation involved.
- Determine the inverse operation: Find the inverse operation to isolate the variable.
- Apply the inverse operation: Perform the inverse operation on both sides of the equation to solve for the variable.
Example Solutions:
- 2x = 6
- Inverse operation: division
- Solution: x = 6 ÷ 2 = 3
- x + 3 = 7
- Inverse operation: subtraction
- Solution: x = 7 - 3 = 4
- x - 2 = 9
- Inverse operation: addition
- Solution: x = 9 + 2 = 11
- x/4 = 9
- Inverse operation: multiplication
- Solution: x = 9 × 4 = 36
One-Step Equation Worksheet
Practice solving one-step equations with the following worksheet:
| Equation | Solution |
|---|---|
| x + 2 = 5 | |
| 3x = 12 | |
| x - 1 = 6 | |
| x/2 = 8 | |
| 2x - 3 = 7 | |
| x + 4 = 11 | |
| 5x = 20 | |
| x - 2 = 4 | |
| 3x - 2 = 10 | |
| x/3 = 9 |
Answer Key
- x + 2 = 5 –> x = 3
- 3x = 12 –> x = 4
- x - 1 = 6 –> x = 7
- x/2 = 8 –> x = 16
- 2x - 3 = 7 –> x = 5
- x + 4 = 11 –> x = 7
- 5x = 20 –> x = 4
- x - 2 = 4 –> x = 6
- 3x - 2 = 10 –> x = 4
- x/3 = 9 –> x = 27
📝 Note: Encourage students to show their work and explain their reasoning for each solution.
In conclusion, one-step equations are fundamental in mathematics, and mastering these equations develops essential problem-solving skills. By practicing with the provided worksheet, students will become proficient in solving one-step equations and build a strong foundation for more complex algebraic equations.
What is a one-step equation?
+A one-step equation is an algebraic equation that requires only one operation to solve, typically involving addition, subtraction, multiplication, or division.
Why are one-step equations important?
+One-step equations are essential in mathematics, as they help build the foundation for more complex algebraic equations and develop problem-solving skills, critical thinking, and logical reasoning.
How do I solve one-step equations?
+To solve one-step equations, identify the variable, constants, and the operation involved, determine the inverse operation, and apply the inverse operation on both sides of the equation to isolate the variable.
