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Introduction
Solving two-step equations is a fundamental concept in algebra that requires a combination of addition, subtraction, multiplication, and division operations to isolate the variable. In this article, we will guide you through the process of solving a two-step equation using a unique approach that involves dragging tiles to fill empty slots and reveal the next step in the solution.
Understanding Two-Step Equations
A two-step equation is a linear equation that requires two operations to solve for the variable. It typically takes the form of:
ax + b = c
where a, b, and c are constants, and x is the variable. To solve for x, we need to isolate it on one side of the equation by performing two operations: addition, subtraction, multiplication, or division.
The Tile-Based Approach
The tile-based approach is a visual representation of the solution process that involves dragging tiles from the left to fill empty slots and reveal the next step in the solution. This approach helps to make the solution process more intuitive and easier to understand.
Step 1: Write the Equation
The first step is to write the equation on a piece of paper or a whiteboard. In this case, the equation is:
14 = 31.7 - 3x
Step 2: Identify the Empty Slots
The next step is to identify the empty slots in the equation. In this case, the empty slots are the x variable and the constant term on the right-hand side of the equation.
Step 3: Drag Tiles to Fill Empty Slots
To fill the empty slots, we need to drag tiles from the left to the right. The tiles represent the operations that we need to perform to solve for x. In this case, we need to drag a tile that represents the multiplication operation (3x) to the right to fill the empty slot.
Step 4: Perform the First Operation
Once we have dragged the tile to the right, we need to perform the first operation, which is to subtract 3x from 31.7. This will give us:
31.7 - 3x = 14
Step 5: Perform the Second Operation
The next step is to perform the second operation, which is to add 3x to both sides of the equation. This will give us:
31.7 = 14 + 3x
Step 6: Solve for x
The final step is to solve for x by isolating it on one side of the equation. To do this, we need to subtract 14 from both sides of the equation, which will give us:
17.7 = 3x
Next, we need to divide both sides of the equation by 3 to solve for x:
x = 17.7 / 3
x = 5.9
Conclusion
Solving two-step equations requires a combination of addition, subtraction, multiplication, and division operations to isolate the variable. The tile-based approach is a visual representation of the solution process that involves dragging tiles to fill empty slots and reveal the next step in the solution. By following these steps, we can solve two-step equations and find the value of the variable.
Frequently Asked Questions
Q: What is a two-step equation?
A: A two-step equation is a linear equation that requires two operations to solve for the variable.
Q: How do I solve a two-step equation?
A: To solve a two-step equation, you need to perform two operations: addition, subtraction, multiplication, or division.
Q: What is the tile-based approach?
A: The tile-based approach is a visual representation of the solution process that involves dragging tiles to fill empty slots and reveal the next step in the solution.
Q: How do I use the tile-based approach to solve a two-step equation?
A: To use the tile-based approach, you need to write the equation, identify the empty slots, drag tiles to fill the empty slots, perform the first operation, perform the second operation, and solve for x.
Example Problems
Problem 1:
Solve the two-step equation:
2x + 5 = 11
Solution:
2x = 11 - 5 2x = 6 x = 6 / 2 x = 3
Problem 2:
Solve the two-step equation:
x - 2 = 7
Solution:
x = 7 + 2 x = 9
Tips and Tricks
Tip 1:
When solving two-step equations, make sure to perform the operations in the correct order.
Tip 2:
Use the tile-based approach to visualize the solution process and make it easier to understand.
Tip 3:
Check your work by plugging the solution back into the original equation to ensure that it is true.
Conclusion
Solving two-step equations is a fundamental concept in algebra that requires a combination of addition, subtraction, multiplication, and division operations to isolate the variable. The tile-based approach is a visual representation of the solution process that involves dragging tiles to fill empty slots and reveal the next step in the solution. By following these steps and using the tile-based approach, we can solve two-step equations and find the value of the variable.
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Introduction
Solving two-step equations can be a challenging task, especially for students who are new to algebra. In this article, we will answer some of the most frequently asked questions about two-step equations and provide tips and tricks to help you solve them.
Q&A
Q: What is a two-step equation?
A: A two-step equation is a linear equation that requires two operations to solve for the variable. It typically takes the form of:
ax + b = c
where a, b, and c are constants, and x is the variable.
Q: How do I solve a two-step equation?
A: To solve a two-step equation, you need to perform two operations: addition, subtraction, multiplication, or division. The order of operations is important, and you should follow the order of operations (PEMDAS) to ensure that you are solving the equation correctly.
Q: What is the tile-based approach?
A: The tile-based approach is a visual representation of the solution process that involves dragging tiles to fill empty slots and reveal the next step in the solution. This approach helps to make the solution process more intuitive and easier to understand.
Q: How do I use the tile-based approach to solve a two-step equation?
A: To use the tile-based approach, you need to write the equation, identify the empty slots, drag tiles to fill the empty slots, perform the first operation, perform the second operation, and solve for x.
Q: What are some common mistakes to avoid when solving two-step equations?
A: Some common mistakes to avoid when solving two-step equations include:
- Not following the order of operations (PEMDAS)
- Not isolating the variable on one side of the equation
- Not checking your work by plugging the solution back into the original equation
Q: How do I check my work when solving a two-step equation?
A: To check your work, you need to plug the solution back into the original equation and verify that it is true. This will help you to ensure that you have solved the equation correctly.
Q: What are some tips and tricks for solving two-step equations?
A: Some tips and tricks for solving two-step equations include:
- Using the tile-based approach to visualize the solution process
- Following the order of operations (PEMDAS)
- Checking your work by plugging the solution back into the original equation
- Using algebraic properties, such as the distributive property, to simplify the equation
Example Problems
Problem 1:
Solve the two-step equation:
2x + 5 = 11
Solution:
2x = 11 - 5 2x = 6 x = 6 / 2 x = 3
Problem 2:
Solve the two-step equation:
x - 2 = 7
Solution:
x = 7 + 2 x = 9
Tips and Tricks
Tip 1:
When solving two-step equations, make sure to perform the operations in the correct order.
Tip 2:
Use the tile-based approach to visualize the solution process and make it easier to understand.
Tip 3:
Check your work by plugging the solution back into the original equation to ensure that it is true.
Conclusion
Solving two-step equations can be a challenging task, but with the right approach and techniques, it can be made easier. The tile-based approach is a visual representation of the solution process that involves dragging tiles to fill empty slots and reveal the next step in the solution. By following these steps and using the tile-based approach, you can solve two-step equations and find the value of the variable.
Frequently Asked Questions
Q: What is a two-step equation?
A: A two-step equation is a linear equation that requires two operations to solve for the variable.
Q: How do I solve a two-step equation?
A: To solve a two-step equation, you need to perform two operations: addition, subtraction, multiplication, or division.
Q: What is the tile-based approach?
A: The tile-based approach is a visual representation of the solution process that involves dragging tiles to fill empty slots and reveal the next step in the solution.
Q: How do I use the tile-based approach to solve a two-step equation?
A: To use the tile-based approach, you need to write the equation, identify the empty slots, drag tiles to fill the empty slots, perform the first operation, perform the second operation, and solve for x.
Additional Resources
Conclusion
Solving two-step equations is an important skill that requires practice and patience. By following the steps outlined in this article and using the tile-based approach, you can solve two-step equations and find the value of the variable. Remember to check your work by plugging the solution back into the original equation to ensure that it is true.